kronecker products of representations of exceptional lie groups a technique is described for evaluating kronecker products of irreducible representations of an exceptional lie group g the method depends upon the natural embedding in g of a classical lie subgroup h the problem is reduced to that of finding the branching of one irreducible representation of g on restriction to h evaluating kronecker products in h and finally using the modification rules appropriate to g

irreducible representations of brauer algebras irreducible representations of brauer algebras are constructed by using the induced representation and the linear equation method as examples some matrix representations of brauer algebras df n with f or 5 are presented

branching index sum rules for simple lie algebras let l and l0 be a simple lie algebra and its sub lie algebra respectively then a given irreducible representation of l decomposes into a direct sum of irreducible components of l0 which is called the branching rule the general dynkin indices introduced earlier satisfy many sum rules for the branching rule these are found to be strong enough to uniquely determine the branching rule for many cases we have studied the sum rules are especially useful for cases of exceptional lie algebras

subduction coefficients of brauer algebras and racah coefficients of o n and sp 2 m ii racah coefficients irreducible representations of brauer algebras are discussed in the non standard basis a method for evaluating subduction coefficients sdcs i e the transformation coefficients between standard and non standard bases of brauer algebras is outlined non trivial sdcs of for are derived racah coefficients of o n and sp 2m can be derived from subduction coefficients of brauer algebras by using the schur weyl duality relation between and o n or sp 2m

inverse branching rules a method is given for inverting branching rules which is based on a technique for computing kronecker products due to king 1981 this approach simplifies the calculation of plethysms and branching rules of representations of exceptional groups it may also be applied to basic spin plethysms

young tableau methods for kronecker products of representations of the classical groups diagrammatic methods for decomposing kronecker products of arbitrary representations of any of the classical groups are presented for convenience efficient ways of computing the dimensions and quadratic casimir s c2 r are also given these methods seem more useful for hand calculations than the method of schur functions or characteristic polynomials an appendix presents the kronecker products for any two representations of dimension 100

the induced representations of brauer algebras and the clebsch gordan coefficients of induced representations of from with are discussed the induction coefficients idcs or the outer product reduction coefficients of with up to a normalization factor are derived by using the linear equation method weyl tableaux for the corresponding gel fand basis of so n are defined the assimilation method for obtaining clebsch gordan coefficients of so n in the gel fand basis for no modification rule involved couplings from idcs of brauer algebras is proposed some isoscalar factors of for the resulting irrep with are tabulated

integrators for lie poisson or dynamical systems abstract we reformulate the ge marsden 1988 lie poisson integration algorithm in terms of algebra variables alone and show how to implement it for regular quadratic lie algebras to arbitrary order and for arbitrary lie algebras to first order we also describe two generalizations of ruth s method 1983 that can be used to generate very fast algorithms

composite young diagrams supercharacters of u m n and modification rules the supercharacter of u m n associated with an arbitrary composite young diagram is defined the distinction is made between standard and non standard supercharacters a modification rule is presented which may be used to express any non standard supercharacter in terms of standard supercharacters in the case n 0 the rule reduces to the rule already known to be appropriate to u m

invariant affine connections on lie groups the space of bi invariant affine connections is determined for arbitrary compact lie groups in particular there is a surprising new family of such connections on su n

algebraic solution for the vector potential in the dirac equation the dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential radford s method of algebraically solving for the vector potential is reviewed with attention to the additional constraints arising from non maximality of the rank the extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c and a number wavefunctions pacs numbers 0350d 0210 0220 0365p 1130p

further results on high rate punctured convolutional codes for viterbi and sequential decoding the weight spectra of high rate lpunctured convolutional codes are evaluated under the hypothesis of a low rate structure this interpretation yields results slightly different from those obtained when weight spectra are evaluated assuming a true high rate structure for punctured codes the search for long memory punctured codes is extended by providing new punctured codes of rates 4 5 5 6 6 7 and 7 8 with memories ranging from 9 to 19

calabi yau manifolds motivations and constructions the possible ways of compacitification of thee8 e8 superstring theory to four dimensions are reviewed the phenomenological need forn 1 supersymmetry is argued on quite general grounds to favour the choice of a calabi yau manifold for the compact internal manifold the massless spectrum after compactification is derived in full detail revealing beside the usual particles others that may have great phenomenological impact the technical aspects of the construction of such manifolds are examined and the methods of calculation of the relevant topological properties are given a big family of such constructions giving rise to many new calabi yau manifolds is presented and its relevance to the search of a phenomenologically acceptable solution is discussed

holomorphic discrete series and harmonic series unitary irreducible representations of non compact lie groups sp 2n r u p q and so 2n generalised characters of the infinite dimensional holomorphic discrete series unitary irreducible representations of the non compact groups u p q sp 2n r and so 2n are explicitly expressed in terms of characters of finite dimensional unitary group representations these formulae are remarkably succinct despite involving certain infinite series of schur functions similar formulae are derived for harmonic series unitary representation of both u p q and sp 2n r consideration of the branching rules from u p q to u q p and from sp 2n r to u n enables holomorphic representations to be identified as a subset of the harmonic representations the branching rules are established in full generality and are then used in the evaluation of tensor products of both holomorphic and harmonic representations in the case of the former a known result is recast in terms of closed formulae involving schur functions and for the latter various generalisations of these formulae are given a conjecture is also made regarding what might be the simplest possible formulae covering all holomorphic and harmonic representations of sp 2n r and u p q illustrative examples are presented

a search for good convolutional codes to be used in the construction of turbo codes recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes we recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes tables of the best recursive systematic convolutional encoders found are presented for various rates together with the average bit error probability performances of some turbo codes using them

the induction coefficients of the hecke algebra and the clebsch gordan coefficients of the quantum group suq n i special gel fand basis a general procedure for evaluating the induction coefficients idcs or the outer product reduction coefficients of the hecke algebra hf q of the af 1 type is formulated based on the linear equation method analytical expressions for the idc s of hf q are tabulated for f 4 it is also proved that these idcs are the clebsch gordan coefficients for the special gel fand basis of the quantum group suq n

young diagrams supercharacters of osp m n and modification rules the supercharacter of osp m n associated with an arbitrary young diagram is defined the distinction is made between osp m n standard and non standard supercharacters the corresponding modification rule which may be used to express a non standard supercharacter in terms of standard supercharacters is presented exemplified and proved this rule involves the removal of n 2 1 boundary strips from the young diagram in the case n 0 the rule reduces to the well known rule appropriate to o m for a non standard supercharacter corresponding to a typical irreducible representation of osp m n the modification yields a single typical standard supercharacter on the other hand for a non standard supercharacter corresponding to an atypical irreducible representation the rule yields a linear combination of atypical standard supercharacters

s function series revisited a systematic and readily programmable computational method is given to extract the s function content of any arbitrary symmetric polynomial function applications to the derivation of new series and the outer product or skew division of an s function by a series are shown

extended poincare supersymmetry rotation groups and branching rules the decomposition of the basic spin irreps of the special orthogonal group so2k into irreps of sod 2 k where d is the spacetime dimension of the extended d dimensional poincare supersymmetry and k is the appropriate automorphism group is determined general results for d 10 several new branching rules for subgroups of so2k are developed a number of specific results are tabulated

young diagrammatic methods for the representation theory of the classical groups of type bn cn dn since the appearance of the celebrated article the classical groups of weyl 7 numerous influences have occurred in the representation theory of the classical groups especially it has become folklore that the facts in this field should be expressed only in terms of young diagrams the aim of this paper is one of the realizations of this principle a classical model of our approach is the results for gl n which are known as littlewood richardson coefficients and the kostka coefficients these two coefficients can be stated in the combinatorial manner using only young diagrams independently of the rank n of gl n we generalize these results to the other classical groups over c namely we give explicit formulas to decompose the tensor product of two irreducible representations into irreducible constituents also we have obtained an interesting relationship linking the irreducible characters of sp and so which we call duality relation between the representations of sp and so as for explicit formulas for the multiplicities of weights in the form of polynomials in the rank n we refer to 3

spectrum generating functions for strings and superstrings the spectrum generating functions for a variety of strings and superstrings are derived these are expressed in terms of characters of irreducible representations of the appropriate transverse spacetime symmetry group and in the case of heterotic strings the relevant gauge group e8 e8 or spin 32 z2 the expansions involve principal specialisations of characters of both gl n and gl m n in the limit as m and n tend to infinity by using schur function methods modification rules and various theta function identities a number of spectrum generating functions are derived and tabulated the equivalence of the gso projected neveu schwarz ramond superstring and the green schwarz superstring is proved and the connection between the lattice formulation and the gso projected neveu schwarz ramond formulation of heterotic strings is spelled out

symmetrised powers of rotation group representations the results given permit the unambiguous evaluation of all possible kronecker products of the irreducible representations tensor and spinor of on and son for n 2 nu and n 2 nu 1 a complete resolution of the second and third powers of the basic spinor representations of so2 nu and so2 nu 1 is given together with a prescription for analysing the fourth power of these representations detailed application is made to the enumeration of properties of so10 relevant to grand unified theories and sufficient information given to resolve the fourth power of any representation of so10

upper bounds for multiplicities in a tensor product of representations and in a restriction of group representations to a subgroup upper bounds for multiplicities of irreducible representations of a semisimple compact lie group in the tensor product of representations and multiplicities of irreducible representations of a subgroup in an irreducible representation of a group are derived pairs of groups and subgroups appear from the representation theory of non compact groups

vertex operators and composite supersymmetric s functions the s function basis for the fock space of vertex operator constructions is considered where states are associated with partitions mod lambda the authors show that the matrix element lambda mod valpha z mod mu is essentially given by the composite s function slambda mu z where the argument z identical to z 1 is replicated mod alpha mod times matrix elements of products of vertex operators lambda mod valpha z v beta w mod mu are given up to functions of z w independent of lambda and mu by the composite supersymmetric s function slambda mu z w where the z w are replicated mod alpha mod mod beta mod times the supersymmetric arguments being those associated with negative roots

symmetric and unitary group representations i duality theory an extension of the schur weyl duality connecting the representations of the symmetric and unitary groups is given the schur weyl basis is constructed using annihilation and creation operators three factorisation lemmas are derived their importance lies in the fact that they relate the phase freedoms within the racah wigner algebra of the symmetric groups and the unitary groups extensions of the regge symmetries are also given these are expressed in five duality relations

crystal graphs for representations of the q analogue of classical lie algebras the explicit form of the crystal graphs for the finite dimensional representations of the q analogue of the universal enveloping algebras of type a b c and d is given in terms of semi standard tableaux and its analogues

new example of a generating function for wznw fusion rules the authors review the construction of generating functions for wznw wess zumino novikov witten fusion rules and present the explicit form of the generating function for so 5 in addition to providing a compact and manifestly positive expression for the so 5 fusion rules at all levels this result illustrates a general conjecture on the relation between the generating function for wznw fusion rules and that for finite lie algebra tensor products

finite dimensional lie poisson approximations to vlasov poisson equations many of the basic equations of conservative continuum mechanics euler vlasov poisson vlasov maxwell mhd etc are hamiltonian systems with respect to lie poisson brackets on dual spaces of infinite dimensional lie algebras the development of lie poisson integrators for finite dimensional lie poisson systems has shown that they are superior in the numerical simulations of these systems especially with regard to long term phenomena this paper shows how to truncate one of these systems the vlasov poisson equation of plasma physics to a finite dimensional lie poisson system this requires replacing the functions on single particle phase space with their poisson bracket lie algebra structure by a finite dimensional lie algebra replacing the densities by their moments of order up to k about a fixed reference point corresponds to replacing the functions by their taylor expansions up to order k unfortunately these truncated taylor expansions do not form a lie algebra since the functions which vanish through order k do not form an ideal under poisson bracket geometrically this corresponds to the fact that canonical transformations which fix the reference point do not form a normal subgroup introducing the location of a reference point in phase space as an extra variable and truncating with respect to this moving point turns out to decouple the location from shape coordinates of a lump of density in phase space as far as the poisson bracket is concerned one can then replace the shape coordinates by a finite number of moments the central result of the paper is a construction of the decoupling map described above in the general context of the decomposition of a lie group as a product of subgroups the main theorem is first proved by the general theory of poisson reduction then by explicit calculation and lastly by showing that the poisson isomorphism follows from the lift of a natural groupoid isomorphism the groupoid aspect of the theory also provides natural poisson maps useful in the application of ruth type integration techniques which do not seem easily derivable from the general theory of poisson reduction 1994 john wiley sons inc

the representation space of the nuclear symplectic sp 6 r shell model the problem of obtaining the sp 6 r irreducible representations that arise from the symmetrized products of a copies of the fundamental representation of sp 6 r is considered a simple method is developed that rapidly leads to the determination of the sp 6 r content up to a prescribed cut off in practical calculations a is identified with the nucleon number it is shown that for a given excitation energy cut off n omega and sufficiently large a the number and multiplicities of the sp 6 r irreducible representations is fixed and the content can be expressed in an a independent manner complete results are given for n or 16 there is no difficulty in principle in going to higher excitations and details are given for determining the sp 6 r content for a or 16

the theory of angular momenta and higher su n symmetries the authors discuss interrelations between generating invariants gi for the reduction pi mi 1 d pi to d on 1 of the m fold tensor product of su n irreducible representations irreps d pi and polynominal bases of the su m irreps d on 1j om n 1 ok 0 0 0 k times a realisation of the su m irrep d oj om 3 bases is given in terms of gi for su 2 coupling wigner coefficients as a byproduct an expression is obtained for su 2 6 j symbols in terms of only two wigner coefficients the authors also discuss some possibilities of the analysis involved in solving the wigner biedenharn problem construction of orthonormal sets of the wigner coefficients for su n groups n or 3

new short constraint length convolutional code constructions for selected rational rates corresp new short constraint length convolutional code constructions are tabulated for rates r n k n k 1 2 cdots n 1 with n 2 3 cdots 8 and for constraint lengths k 3 4 cdots 8 these codes have been determined by iterative search based upon a criterion of optimizing the free distance profile specifically these codes maximize the free distance d f while minimizing the number of adversaries in the distance or weight spectrum in several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length these codes are expected to have a number of applications including combined source channel coding schemes as well as coding for burst or impulsive noise channels

demazure characters and wzw fusion rules the demazure character formula is applied to the verlinde formula for the fusion rules of wess zumino witten wzw models we follow littelmann s derivation of a generalized littlewood richardson rule that computes tensor products for simple lie algebras a combinatorial rule for wzw fusions does not result however only a modified version of the littlewood richardson rule is obtained that computes an old upper bound on the fusion coefficients of ar wzw models we argue that this is because the characters of simple lie algebras appear in this treatment instead of the corresponding affine characters the bruhat order on the affine weyl group must be implicated in any combinatorial rule for wzw fusions the bruhat order on subgroups of this group such as the finite weyl group does not suffice

a classification of multiplicity free actions abstract the action of a complex algebraic groupgon an affine varietyvis said to be multiplicity free if each irreducible representation ofgoccurs at most once in the ring c v of regular functions onv this paper concerns the classical setting wherevis a vector space andgacts linearly onv the irreducible linear multiplicity free actions have been classified by v kac the focus here is on nonirreducible linear multiplicity free actions we exhibit many such actions which do not decompose as direct products of irreducible actions our main results provide a classification for all linear multiplicity free actions on a vector space

evasion with weak superiority le but du poursuivant est de terminer le jeu en choisissant une commande convenable alors que le but de l echappant est d empecher la fin du jeu avec une commande appropriee

the complete matter sector in a three generation compactification we consider a calabi yau compactification paradigm with three light generations and anr symmetry from a special form of the tian yau manifold we also construct a new three generation model with markedly different phenomenology thecomplete spectrum of all light matter fields is obtained in a universal way and moreover in a physically suitable basis allowing a straightforward analysis of all their couplings here we discuss all the renormalizable yukawa couplings this computation can equally well be repeated for all compactification models based on calabi yau complete intersections in products of homogeneous spaces

branching rules for e8 so16 branching rules for e8 down arrow so16 are derived from those of e8 down arrow su2 e7 down arrow su8 and so16 down arrow u1 su8 by noting that both group chains share a common u1 su8 subgroup additional branching rules are deduced from kronecker products of e8 and so16 irreps in each case the rules distinguish unambiguously between conjugate irreps of so16 an alternative labelling scheme for the irreps of so2k based on its maximal u1 suk subgroup is outlined

the tangent bundle of a calabi yau manifold deformations and restriction to rational curves the tangent bundle x of a calabi yau threefoldx is the only known example of a stable bundle with non trivial restriction to any rational curve onx by deforming the direct sum of x and the trivial line bundle one can try to obtain new examples we use algebro geometric techniques to derive results in this direction the relation to the finiteness of rational curves on calabi yau threefolds is discussed

unitary representations branching rules and matrix elements for the non compact symplectic groups the complementarity of the symplectic and orthogonal groups is used to infer properties of the infinite dimensional unirreps of the former from the character theory of the latter the complete set of d series metaplectic unirreps of sp n r is identified and branching rules are given for their restrictions to the maximal compact subgroup u n developed in terms of the properties of schur functions a known algorithm for the evaluation of matrix elements of the sp 3 r lie algebra is extended to any sp n r and analytic expressions are given for important classes of unirreps and multiplicity free states

polynomial deformations and cohomology of calabi yau manifolds we study the method of polynomial deformations that is used in the physics literature to determine the hodge numbers of calabi yau manifolds as well as the related yukawa couplings we show that the argument generally presented in the literature in support of these computations is seriously misleading give a correct proof which applies to all the cases we found in the literature and present examples which show that the method is not universally valid we present a general analysis which applies to all calabi yau manifolds embedded as complete intersections in products of complex projective spaces yields sufficient conditions for the validity of the polynomial deformation method and provides an alternative computation of all the hodge numbers in many cases in which the polynomial method fails

branching rules for irreducible representations of e8 into d8 the branching rules for irreducible representations of e8 into d8 are calculated using the knowledge of the kronecker products for those two algebras tables of kronecker products for both e8 and d8 algebras are also included

natural labelling schemes for simple roots and irreducible representations of exceptional lie algebras the simple root system of each exceptional simple lie algebra is explicitly constructed in a variety of forms each construction is based on the natural embedding in the exceptional algebra of a classical semi simple algebra of the same rank the procedure adopted leads to the discovery of a number of new chains of subalgebras illustrated by means of supplemented dynkin diagrams the various sets of simple roots are then used to determine natural labels for the irreducible representations of each of the exceptional algebras for each such labelling scheme the modification rules for dealing with non standard representation labels are tabulated the connection between the natural labels and dynkin labels is given in detail and a comparison is made with the labels of b g wybourne and m j bowick 1977

stabilization of nonlinear large scale uncertain dynamical systems abstract the notions of ultimate stabilizability and asymptotical stabilizability by local feedback strategies for nonlinear large scale systems are introduced under some structural conditions on the interconnected subsystems we obtain the ultimate stabilizability and the asymptotical stabilizability of the system by local feedback strategies

a generalization of the littlewood richardson rule for the general linear group gz the littlewood richardson rule see 18 193 gives a method to calculate the decomposition of a tensor product of two irreducible g representations the aim of this article is to give a generalization of this rule for all simple simply connected algebraic groups of type a b c d g2 and e we obtain also partial results for g of type f4 e and es the restrictions in the last three cases come from the fact that for the formulation of the decomposition rules we need the notion of a standard young tableau such a notion has been developed by seshadri lakshmibai musili and rajeswari in a series of articles see ll 13 14 16 but not yet for all representations of the last three exceptional groups the advantage of the notion of a young tableau developed by seshadri et al is that it is independent of the type of the group for the convenience of the reader not used to this notion we give first a seperate proof for g sz using the classical notion of a standard young tableau of course for applications the classical notion is much more appropriate in the appendix we give a translation of the notion of a standard young tableau in the sense of seshadri et al into the classical notion of a young tableau for g sp2 and spin in 3 8 we give also such a translation for g g for the other exceptional groups such a translation is not known to the author let p be a dominant weight for g and denote by i the corresponding simple g module we assume that the character of vp is given by ct eycr where the sum has to be taken over all standard young tableaux f of shape p p and v 5 is the weight of the tableau y now by the

kronecker products for so 2p representations a relatively simple algorithm for the decomposition of the product of two so 2p representations is presented for this purpose generalised young tableaux are introduced and their product is defined

character calculations for semisimple lie algebras a recursive method for calculation of characters of semisimple lie algebras is outlined by slight modifications algorithms are obtained for the computation of weight multiplicities kronecker products and branching rules as well as symmetrized kronecker powers

high rate punctured convolutional codes structure properties and construction technique the authors present some properties of punctured convolutional codes providing a construction method and a list of new good high rate long memory punctured codes the structure of punctured codes is examined and an upper bound on the free distance of punctured codes is derived indicating that punctured codes are good codes a construction method that generates the low rate original codes which duplicate given known high rate codes through perforation is proposed tables of punctured codes that duplicate the best known nonsystematic codes of rates 2 3 and 3 4 with memory lengths ranging from 3 to 23 and from 3 to 9 respectively are given together with the best known systematic codes for rates ranging from 2 3 to 7 8 with very long memory m 44 through 48

simultaneity and reality of u n and su n 3jm and 6j symbols a simple proof is given of the simultaneous existence of a real set of 3jm and 6j symbols for the unitary groups u n and su n including the case of mixed tensor representations we observe that simultaneity is incompatible with the conventional permutation symmetries for u n with n 3 the relevance of these results to the schur weyl duality of u n with the symmetric groups sl is discussed

decomposition of the polynomial kernel of arbitrary higher spin dirac operators in a series of recent papers we have introduced higher spin dirac operators which are generalisations of the classical dirac operator whereas the latter acts on spinor valued functions the former acts on functions taking values in arbitrary irreducible half integer highest weight representations for the spin group in this paper we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group we will hereby make use of results from representation theory

the weyl groups and weight multiplicities of the exceptional lie groups the weyl group wg of each exceptional simple lie group g is described in detail its structure is defined in terms of its coset decomposition with respect to the weyl group wh of a classical semi simple lie group h embedded naturally in g the concepts of g dominance and g equivalence are defined and used to determine from the character formula of weyl the branching rule associated with the restriction of group elements from g to h the weyl group wg is used further to impose constraints on both the branching multiplicities for g to h and the weight multiplicities of g these constraints are used to evaluate the weight multiplicities of f4 e6 e7 and e8 together with the branching multiplicities for e8 to so 16

new s function series and non compact lie groups a number of new infinite series of s functions are described in terms of their generating functions and s function content applications to the character theory of non compact lie groups are noted

a new young diagrammatic method for kronecker products of and a new simple young diagrammatic method for kronecker products of o n and sp 2m is proposed based on the representation theory of brauer algebras a general procedure for the decomposition of the tensor products of representations for o n and sp 2m is outlined which is similar to that for u n known as the littlewood rules together with trace contractions from a brauer algebra and some modification rules given by king

punctured convolutional codes for the 1 d partial response channel a coded 1 d system containing a punctured convolutional encoder is analyzed in general a punctured encoder with 2 sup v states results in a decoder trellis with 2 sup v 1 states and a periodically time varying branch structure a class c of punctured convolutional encoders for which the decoder trellis has a fixed branch structure with 2 sup v states is described an encoder in this class can be combined with a precoder to form a new punctured convolutional encoder that generates the output from the precoder the author determines the set of good variable rate trellis codes for selectable rate encoding and viterbi decoding a set of variable rate trellis codes is generated by a variable rate punctured convolutional encoder in c the author also determines punctured convolutional encoders in c that generate a single good high rate trellis code

racah coefficients of quantum group uq n racah coefficients of uq n are derived from subduction coefficients of hecke algebras hf q by using the schur weyl duality relation between uq n and hf q the racah coefficients of uq n for the resulting irreps n1 n2 nk o with sigma i 1kni or 5 and some of them for the resulting irreps with multiplicity and sigma i 1kni or 6 are tabulated

endomorphism valued cohomology and gauge neutral matter for several physically interesting calabi yau manifolds we count and parametrize gauge neutral matter particles occurring in corresponding superstring compactifications to this end we use the technique of exact and spectral sequences and then describe and discuss our results in the more familiar tensor notation

some extended results on the search for good convolutional codes we provide useful results on two classes of convolutional codes binary codes and nonbinary codes the best codes or the best known codes for these two classes of convolutional codes are found by computer search some of them are better than those found in the past we specify these codes by their transfer function matrices distance spectra and information weight spectra furthermore we derive an upper bound on the free distances of binary to m ary codes and q ary to m ary codes numerical values of this bound closely fit the computer searched values

kronecker products for compact semisimple lie groups a review is given of the application of s function techniques to the evaluation of kronecker products of irreducible representations of compact semisimple lie groups explicit formulae are derived for all irreducible representations of all such groups recent developments involving composite young diagrams are brought to fruition and the vexed problem of so2k is dealt with completely new branching rules for the classical groups are given in an appendix these are exploited in the evaluation of kronecker products by means of a technique which is applied to both classical and exceptional groups a discussion is made of various modification rules which are needed to express the final results in standard form

young supertableaux of the basic lie superalgebras among the simple lie superalgebras lsa the basic classical ones are well known together with many of their finite dimensional representations this is particularly true for the typical representations which are known to be completely reducible it is well known that reducible but indecomposable representations of the basic lsa are not completely characterised by their highest weight hw or the eigenvalues of their casimir operators in fact there may be several different finite representations characterised by the same hw such representations are called non typical or atypical the aim of this paper is to establish a complete characterisation of the typical and non typical representations by means of properly defined young supertableaux yst therefore the definition we are going to use for our yst differs slightly from the standard definitions the examples given throughout this paper help the illustration of this new interpretation for the yst which makes possible the complete classification of the indecom posable representations characterised by a generalised notion of hw

heisenberg weyl algebras of symmetric and antisymmetric bosons all the polynomials in symmetric 2 and antisymmetric 11 u n bosons are constructed in u n bases and u n reduced matrix elements for the bosons between polynomial basis states are computed applications to representation theory of lie groups paired fermion and boson physics are briefly discussed

universal integrals of motion and universal invariants of quantum systems universal quantum integrals of motion are introduced and their relation with the universal quantum invariants is established the invariants concerned are certain combinations of the second and higher order moments variances of quantum mechanical operators which are preserved in time independently of the concrete form of the coefficients of the schr dinger equation provided the hamiltonian is either a generic quadratic form of the coordinate and momenta operators or a linear combination of generators of some finite dimensional algebra in particular any semisimple lie algebra using the phase space representation of quantum mechanics in terms of the wigner function the relations between the quantum invariants and the classical universal integral invariants by poincar and cartan are elucidated examples of the universal invariant solutions of the schr dinger equation i e self consistent eigenstates of the universal integrals of motion are given applications to the physics of optical and particle beams are discussed

stable branching rules for classical symmetric pairs we approach the problem of obtaining branching rules from the point of view of dual reductive pairs specifically we obtain a stable branching rule for each of 10 classical families of symmetric pairs in each case the branching multiplicities are expressed in terms of littlewood richardson coefficients some of the formulas are classical and include for example littlewood s restriction rule as a special case

moment invariants for the vlasov equation moment invariants functions of the moments of a vlasov distribution that are invariant under sp 6 are classified using young diagrams the connection between the moment invariants and the poincare invariants is established an application using the moment invariants as phase space coordinates is considered for a matching section in a particle beam accelerator and a lie poisson numerical integration algorithm for the moment dynamics is proposed

covariance correlation and entanglement some new identities for quantum variance and covariance involving commutators are presented in which the density matrix and the operators are treated symmetrically a measure of entanglement is proposed for bipartite systems based upon covariance this works for two and three component systems but produces ambiguities for multicomponent systems of composite dimension its relationship to angular momentum dispersion for symmetric spin states is described

characters dimensions and branching rules for covariant irreps of u n m the theory of symmetric functions is used to obtain simple expressions for the characters and dimensions of the covariant irreps of the supergroup u n m schur function expressions are given for a number of important branching rules

new branching rules induced by plethysm we derive group branching laws for formal characters of subgroups of leaving invariant an arbitrary tensor t of young symmetry type where is an integer partition the branchings and fixing a vector vi a symmetric tensor gij gji and an antisymmetric tensor fij fji respectively are obtained as special cases all new branchings are governed by schur function series obtained from plethysms of the schur function s by the basic m series of complete symmetric functions and the l m 1 series of elementary symmetric functions our main technical tool is that of hopf algebras and our main result is the derivation of a coproduct for any schur function series obtained by plethysm from another such series therefrom one easily obtains generalized newell littlewood formulae and the algebra of the formal group characters of these subgroups is established concrete examples and extensive tabulations are displayed for and showing their involved and nontrivial representation theory the nature of the subgroups is shown to be in general affine and in some instances non reductive we discuss the complexity of the coproduct formula and give a graphical notation to cope with it we also discuss the way in which the group branching laws can be reinterpreted as twisted structures deformed by highly nontrivial 2 cocycles the algebra of subgroup characters is identified as a cliffordization of the algebra of symmetric functions for formal characters modification rules are beyond the scope of the present paper but are briefly discussed

kronecker product of sp 2n representations using generalised young tableaux using generalised young tableaux the authors obtain an explicit formula for the reduction of the kronecker product of irreducible representations of the symplectic groups this extends a previous work devoted to the case of orthogonal groups

tensor gauge fields in arbitrary representations of gl d mathbb r ii quadratic actions quadratic second order non local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in d dimensional minkowski space are explicitly written in a compact form by making use of levi civita tensors the field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non lagrangian local field equations proposed previously moreover these actions allow a frame like reformulation a la macdowell mansouri without any trace constraint in the tangent indices

calculating endomorphism valued cohomology singlet spectrum in superstring models we present a computational strategy based on exact sequences for determining the dimension of endomorphism valued cohomology groups for complete intersections in complex projective space this cohomology group gives rise to part of the gauge singlet spectrum in superstring compactifications we establish the underlying justification for the known deformation theoretical algorithm and by comparison with the exact sequence method indicate its limitations

calabi yau manifolds as complete intersections in products of complex projective spaces we consider constructions of manifolds withsu 3 holonomy as embedded in products of complex projective spaces by imposing certain homogeneous holomorphic constraints we prove that every such construction leads to one deformation class of manifolds withsu 3 holonomy for a subset of these manifolds we prove simple connectedness address the problem of calculating the second betti number and explicitly calculate it for a class of constructions this establishes a very wide class of manifolds withsu 3 holonomy that can give rise to yet many more constructions via dividing out the action of suitably chosen discrete groups some of the examples studied may yield phenomenologically acceptable models

new short constraint length rate n 1 n punctured convolutional codes for soft decision viterbi decoding punctured convolutional codes with good performance are reported for rates n 1 n with n 5 6 7 8 and constraint lengths k 2 3 6 the tabulated codes are nonsystematic binary convolutional codes with maximum free distance and minimum information weight for use with soft decision viterbi decoding

the hopf algebra structure of the character rings of classical groups the character ring of covariant irreducible tensor representations of the general linear group admits a hopf algebra structure isomorphic to the hopf algebra of symmetric functions here we study the character rings and of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions we show that and also admit natural hopf algebra structures that are isomorphic to that of and hence to the isomorphisms are determined explicitly along with the specification of standard bases for and analogous to those used for a major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic schur hall scalar products significantly the adjoint with respect to multiplication no longer coincides as it does in the case with a foulkes derivative or skew operation the adjoint and foulkes derivative now require separate definitions and their properties are explored here in the orthogonal and symplectic cases moreover the hopf algebras and are not self dual the dual hopf algebras and are identified finally the hopf algebra of the universal rational character ring of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified

su n and sp 2n wzw fusion rules fusion rules for wzw models based on su n and sp 2n are considered using the results of kac 1989 and walton 1989 1990 it is shown that these fusion rules may be computed using young diagram methods by performing extra modifications these modifications take the form of the removal of boundary strips which bear a striking resemblance to the modifications necessary when performing tensor products for these algebras this fact is exploited to exhibit a duality between the fusion rules of su n at level k and su k at level n and also between sp 2n at level k and so 2k at level n the former duality has been discussed in the context of two dimensional statistical mechanics by kuniba and nakanishi 1990 and also by naculich and schnitzer 1990 in the case of wzw models and goodman and wenzl 1989 for hecke algebras at roots of unity for su 3 a manifestly positive combinatorial procedure for computing fusion rules and a generating function for the fusion coefficients are given

an extensive search for good punctured rate k k 1 recursive convolutional codes for serially concatenated convolutional codes in many practical applications requiring variable rate coding and or high rate coding for spectral efficiency there is a need to employ high rate convolutional codes cc either by themselves or in a parallel or serially concatenated scheme for such applications in order to keep the trellis complexity of the code constant and to permit the use of a simplified decoder that can accommodate multiple rates a mother cc is punctured to obtain codes with a variety of rates this correspondence presents the results of extensive search for optimal puncturing patterns for recursive convolutional codes leading to codes of rate k k 1 k an integer to be used in serially concatenated convolutional codes sccc the code optimization is in the sense of minimizing the required signal to noise ratio snr for two target bit error rate ber and two target frame error rate fer values we provide extensive sample simulation results for rate k k 1 sccc codes employing our optimized punctured cc

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

on the evadable sets of differential evasion games abstract the notions of evasion strategies and evadable sets are introduced for a nonlinear differential game with information delay and results about the evadable sets and the strict evadability of the game are obtained a linear case is treated at the end

a hopf laboratory for symmetric functions an analysis of symmetric function theory is given from the perspective of the underlying hopf and bi algebraic structures these are presented explicitly in terms of standard symmetric function operations particular attention is focused on laplace pairing sweedler cohomology for 1 and 2 cochains and twisted products rota cliffordizations induced by branching operators in the symmetric function context the latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type a commentary on related issues in the combinatorial approach to quantum field theory is given