injectivity of compressing maps on primitive sequences over bbz p e let zopf pe be the integer residue ring with odd prime p and integer eges2 for a sequence a over zopf pe one has a unique p adic expansion a a 0 a 1 p a e 1 pe 1 where a i can be regarded as a sequence over zopf p for 0lesilese 1 let f x be a strongly primitive polynomial over zopf pe and g f x pe be the set of all primitive sequences generated f x by over zopf pe recently the authors xuan yong zhu and wen feng qi have proved that for a function phi x0 xe 1 g xe 1 eta x0 xe 2 over zopf p and a b ising f x pe where 2lesdeg glesp 1 phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b to further complete their work we show that such injectivity also holds for deg g 1 that is for a function phi x0 xe 1 xe 1 eta x0 xe 2 over zopf p and a b ising f x pe phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b

the generalized atypical supertableaux of the orthosymplectic groups osp 2 2p the classification and the interpretation of the young supertableaux of the orthosymplectic group osp 2 2p are given a particular emphasis is made on the generalized atypical supertableaux associated to nonfully reducible atypical representations

branching rules for the supergroup su n m from those of su n m the decomposition of representations of supergroups into representations of subgroups is needed in practical applications in this paper we set up and exploit a fruitful one to one correspondence between the lie group branching su n m su n su m u 1 and the supergroup branchings su n m su n su m u 1 and su n1 n2 m1 m2 su n1 m1 su n2 m2 u 1 a simple and useful prescription is discovered for obtaining the su n m branching rules from those of su n m for any representation a large class of examples sufficient for many physical applications we can foresee are explicitly worked out and tabulated

distribution properties of compressing sequences derived from primitive sequences over bbz p e let z pe be the integer residue ring with odd prime p and integer e 2 any sequence a over z pe has a unique p adic expansion a a0 a1 p ae 1 pe 1 where ai can be regarded as a sequence over z p for 0 i e 1 let f x be a strongly primitive polynomial over z pe and a b be two primitive sequences generated by f x over z pe assume x0 xe 1 xe 1 x0 xe 2 is an e variable function over z p with the monomial p 1 2 xe 2 p 1 x1 p 1 not pearing in the expression of x0 x1 xe 2 it is shown that if there exists an s z p such that a0 t ae 1 t s if and only if b0 t be 1 t s for all nonnegative t with i 0 where is an m sequence determined by f x and a0 then a b this implies that for compressing sequences derived from primitive sequences generated by f x over z pe single element distribution is unique on all positions t with t 0 in particular when x0 x1 xe 2 0 it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences

character expansion method for supergroups and extended superversions of the leutwyler smilga and berezin karpelevich integrals we introduce an extension of the character expansion method to the case of supergroups this method allows us to calculate a superversion of the leutwyler smilga integral which to the best of our knowledge has not been calculated before we also use the method to generalize a previously calculated superversion of the berezin karpelevich integral our character expansion method should also allow for the calculation of other supergroup integrals

shift register synthesis modulo m the berlekamp algorithm takes a sequence of elements from a field and finds the shortest linear recurrence or linear feedback shift register that can generate the sequence we present an algorithm which generalizes berlekamp s to the case when the elements of the sequence are integers modulo m where m is an arbitrary but known integer details will be published elsewhere

branching rules for a class of typical and atypical representations of gl m n the irreducible representations of the lie superalgebra gl m n with highest weights of the form 1 2 m are investigated using a recently introduced induced module construction for atypical modules the gl m n gl m n 1 branching rules are obtained and a suitable gel fand tsetlin basis is introduced the class of representations considered includes some multiply atypical irreducible representations of gl m n and all irreducible representations of gl m 1

representations of low rank orthosymplectic superalgebras by superfield techniques representations of lie superalgebras may be realised as functions superfields on graded manifolds suitably chosen onset spaces the technique is illustrated for osp 1 2 and osp 2 2 with a review of well known results and applied in the cases of osp 3 2 and osp 4 2 to construct some classes of irreducible representations

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

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

gelfand tzetlin coordinates for the unitary supergroup the gelfand tzetlin method provides explicit coordinates on the parameter space of the unitary groupu k which make direct evaluations of group integrals possible it is closely related to the gelfand construction of finite dimensional irreducible representations we generalize the gelfand tzetlin method to the unitary supergroupu k1 k2 the coordinates on the parameter space for supergroup integrals and the invariant haar measure are evaluated as an example the supersymmetric harish chandra itzykson zuber integral is calculated a generalized gelfand pattern containing anticommuting variables is introduced which determines the representation

the gel fand basis and matrix elements of the graded unitary group u m n projection operators with correct normalisation are constructed for obtaining the gel fand basis mod nu m of the graded unitary group u m n each u m n gel fand basis vector mod nu m for an f particle system uniquely corresponds to a non standard basis vector mod nu m of the permutation group s f the matrix element of the generator ei 1i of u m n between the two gel fand basis vectors mod nu m and mod nu m is proportional to the overlap between the two non standard basis vectors mod nu m and mod nu m of s f explicit formulae are given for the normalisation constant in the projection operator as well as for the matrix elements of the generator ei 1i of the graded unitary group u m n which is the extension of the gel fand tsetlin formula for the ordinary unitary group u m

analytic bethe ansatz and functional equations associated with any simple root systems of the lie superalgebra sl r 1 s 1 abstract the lie superalgebra sl r 1 s 1 admits several inequivalent choices of simple root systems we have carried out analytic bethe ansatz for any simple root systems of sl r 1 s 1 we present transfer matrix eigenvalue formulae in dressed vacuum form which are expressed as the young supertableaux with some semistandard like conditions these formulae have determinant expressions which can be viewed as quantum analogue of jacobi trudi and giambelli formulae for sl r 1 s 1 we also propose a class of transfer matrix functional relations which is specialization of hirota bilinear difference equation using the particle hole transformation relations among the bethe ansatz equations for various kinds of simple root systems are discussed

branes and supergroups extending previous work that involved d3 branes ending on a fivebrane with theta mathrm ym neq 0 we consider a similar two sided problem this construction in case the fivebrane is of ns type is associated to the three dimensional chern simons theory of a supergroup rm u m n or rm os rm p m 2n rather than an ordinary lie group as in the one sided case by s duality we deduce a dual magnetic description of the supergroup chern simons theory a slightly different duality in the orthosymplectic case leads to a strong weak coupling duality between certain supergroup chern simons theories on mathbb r 3 and a further t duality leads to a version of khovanov homology for supergroups some cases of these statements are known in the literature we analyze how these dualities act on line and surface operators

branching rules for typical and atypical representations of gl n 1 the gl n 1 down arrow gl n gl 1 branching rules are determined for all finite dimensional irreducible typical and atypical representations of gl n mod 1 using a recently introduced induced module construction for atypical modules and confirm those found recently by palev 1988 by another method the lowest weights and characters of the irreducible representations are found and the validity for gl n mod 1 of the character formula conjectured by hughes and king 1987 is confirmed some generalisations and extensions of the method are discussed

mixed supertableaux of the superunitary groups ii su n m the young supertableaux of the superunitary groups are studied we give the conditions on the size of legal supertableaux the type of atypicity for tensor representations which are irreducible making the link between the kac dynkin parameters and those of the supertableau a discussion is given on nonfully reducible representations and generalized atypical supertableaux

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

generating functions and elementary young tableaux when constructing polynomial bases for group representations one is led naturally to consider a stretched product of states elementary multiplets are states that cannot be expressed as the stretched product of any other two states and they can be identified with terms occurring in certain generating functions in this paper the authors define an analogous stretched product of young tableaux together with elementary tableaux these may be used in a manner similar to elementary multiplets to construct generating functions they consider several examples where this method can be applied and in particular give new large n rank free branching rule generating functions for the group subgroup pairs su n su m contained in implied by su n m first four labels non zero so n contained in implied by su n first three labels non zero and sp 2n contained in implied by su 2n first five labels non zero this method of finding these generating functions uses the theory of grobner bases which allows the authors to make precise the notion of compatibility relations or forbidden products of elementary tableaux

compression mappings on primitive sequences over z p sup e let z p sup e be the integer residue ring with odd prime p spl ges 5 and integer e spl ges 2 for a sequence a over z p sup e there is a unique p adic expansion a a sub 0 a spl middot p a sub e 1 spl middot p sup e 1 where each a sub i is a sequence over 0 1 p 1 and can be regarded as a sequence over the finite field gf p naturally let f x be a primitive polynomial over z p sup e and g f x p sup e the set of all primitive sequences generated by f x over z p sup e set spl phi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 1 x sub 0 x sub 1 x sub e 2 spl psi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 2 x sub 0 x sub 1 x sub e 2 where spl eta sub e 2 1 and spl eta sub e 2 2 are arbitrary functions of e 1 variables over gf p and 2 spl les k spl les p 1 then the compression mapping spl phi sub e 1 g f x p sup e spl rarr gf p sup spl infin a spl rarr spl phi sub e 1 a sub 0 a sub e 1 is injective that is a b if and only if spl phi sub e 1 a sub 0 a sub e 1 spl phi sub e 1 b sub 0 b sub e 1 for a b spl isin g f x p sup e furthermore if f x is a strongly primitive polynomial over z p sup e then spl phi sub e 1 a sub 0 a sub e 1 spl psi sub e 1 b sub 0 b sub e 1 if and only if a b and spl phi sub e 1 x sub 0 x sub e 1 spl psi sub e 1 x sub 0 x sub e 1 for a b spl isin g f x p sup e

representations of supergroups an explicit construction of representations of supergroups is given in terms of direct products of covariant and contravariant fundamental representations the rules of supersymmetrization are characterized by extended young supertableaux this constructive approach leads to explicit transformation properties of higher representations as well as to closed explicit formulas for characters from which other invariants such as dimensions and eigenvalues of all casimir operators can be calculated we have applied this approach so far to the supergroups su n m osp n 2m p n for which we have obtained all the representations constructible as direct products of the fundamental defining representations an argument is presented toward the irreducibility of all these representations

anomalies and eigenvalues of casimir operators for lie groups and supergroups an expression for the anomaly of any representation of the su n groups and su n m supergroups is presented some anomaly free complex representations of su n and su n m are pointed out for su n these occur for n 5 and for large dimensions for su n m they already occur for low dimensions also a generating function to obtain the eigenvalues of all casimir operators of su n m is given and an extension to other supergroups is pointed out

the most significant bit of maximum length sequences over spl zopf 2 sup l autocorrelation and imbalance the imbalance and the autocorrelation of the binary sequences in the title are explored by combining the local weil bound with spectral analysis recent estimates on these quantities are improved by a factor of order 2 sup l 2 for large l

graded gauge theory the mathematical background for a graded extension of gauge theories is investigated after discussing the general properties of graded lie algebras and what may serve as a model for a graded lie group the graded fiber bundle is constructed its basis manifold is supposed to be the so called superspace i e the product of the minkowskian space time with the grassmann algebra spanned by the anticommuting lorentz spinors the vertical subspaces tangent to the fibers are isomorphic with the graded extension of the su n lie algebra the connection and curvature are defined then on this bundle the two different gradings are either independent of each other or may be unified in one common grading which is equivalent to the choice of the spin statistics dependence the yang mills lagrangian is investigated in the simplified case the conformal symmetry breaking is discussed as well as some other physical consequences of the model

graded tensor calculus we develop a graded tensor calculus corresponding to arbitrary abelian groups of degrees and arbitrary commutation factors the standard basic constructions and definitions like tensor products spaces of multilinear mappings contractions symmetrization symmetric algebra as well as the transpose adjoint and trace of a linear mapping are generalized to the graded case and a multitude of canonical isomorphisms is presented moreover the graded versions of the classical lie algebras are introduced and some of their basic properties are described

on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers let m be a square free odd integer and z m the integer residue ring modulo m this paper studies the distinctness of primitive sequences over z m modulo 2 recently for the case of m pq a product of two distinct prime numbers p and q the problem has been almost completely solved as for the case that m is a product of more prime numbers the problem has been quite resistant to proof in this paper a partial proof is given by showing that a class of primitive sequences of order 2n 1 over z m is distinct modulo 2 where n is a positive integer besides as an independent interest this paper also involves two distribution properties of primitive sequences over z m which are related closely to our main results

finite dimensional representations of the lie superalgebra sl 1 3 in a gel fand zetlin basis ii nontypical representations in a series of two papers all finite dimensional irreducible representations of the special linear lie superalgebra sl 1 3 are constructed explicit formulas for the generators in an orthonormal gel fand zetlin basis of the even subalgebra gl 3 are given this paper develops a background for constructing the representations expressions for the transformation properties of the basis under the action of the generators are written down within all typical sl 1 3 modules

classification and interpretation of the supertableaux of the orthosymplectic groups osp m 4 the supertableaux of the orthosymplectic group osp m 4 are analyzed and interpreted as representations of the corresponding superalgebras an extension of the results to the general case osp m 2p is proposed

schatten von neumann classes of multilinear forms the authors establish a number of results concerning normed ideals of multilinear forms in banach spaces which extend the theory of trace ideals of operators on hilbert space to such multilinear forms for example it is shown that the dual of the space of compact forms is the space of nuclear forms while the second dual is the space of bounded forms moreover a direct analogue of the schatten p ideals of operators on hilbert space is defined using interpolation techniques and a normal form for compact forms is introduced

representations of orthosymplectic superalgebras ii young diagrams and weight space techniques for pt i see ibid vol 16 p 473 1983 finite dimensional graded tensor representations of osp m n are enumerated via standard young diagrams and their corresponding highest weight and kac dynkin labels are given a uniform set of conditions on the diagram shape necessary and sufficient for atypicality are presented weight space techniques are used to provide a complete analysis of an atypical representations for the low rank cases osp 2 2 osp 3 2 and osp 4 2

extendible polynomials on banach spaces abstract we are concerned with the following question when can a polynomial p e x e and x are banach spaces be extended to a banach space containing e we prove that the polynomials that are extendible to any larger space are precisely those which can be extended to c b e if x is complemented in its bidual and l b e in general we also show that the extendibility is a property that is preserved by aron berner extensions and composition with linear operators we construct a predual of the space of extendible polynomials for the case that x is a dual space

analytic bethe ansatz related to a one parameter family of finite dimensional representations of the lie superalgebra as is well known the type 1 lie superalgebra admits a one parameter family of finite dimensional irreducible representations we have carried out an analytic bethe ansatz related to this family of representations we present formulae which are deformations of previously proposed determinant formulae labelled by a young superdiagram these formulae will provide a transfer matrix eigenvalue in a dressed vacuum form related to the solutions of a graded yang baxter equation which depend not only on the spectral parameter but also on a non additive continuous parameter a class of transfer matrix functional relations among these formulae is briefly mentioned

casimir elements of e lie algebras the classical framework for investigating the casimir elements of a lie algebra is generalized to the case of an e lie algebra l we construct the standard l module isomorphism of the e symmetric algebra of l onto its enveloping algebra and we introduce the harish chandra homomorphism in case the generators of l can be written in a canonical two index form we construct the associated standard sequence of casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

incomplete exponential sums over galois rings with applications to some binary sequences derived from z sub 2 sup l an upper bound for the incomplete exponential sums over galois rings is derived explicitly based on the incomplete exponential sums we analyze the partial period properties of some binary sequences derived from z sub 2 sup l in detail such as the kerdock code binary sequences and the highest level sequences of primitive sequences over z sub 2 sup l the results show that the partial period distributions and the partial period independent r pattern distributions of these binary sequences are asymptotically uniform nontrivial upper bounds for the aperiodic autocorrelation of these sequences are also given

a lindenstrauss theorem for some classes of multilinear mappings abstract under some natural hypotheses we show that if a multilinear mapping belongs to some banach multilinear ideal then it can be approximated by multilinear mappings belonging to the same ideal all whose arens extensions attain their norms at the same point we prove a similar result for the class of symmetric multilinear mappings we see that the quantitative bollobas type version of these results fails in every multilinear ideal

on algebras of holomorphic functions of a given type we show that several spaces of holomorphic functions on a riemann domain over a banach space including the nuclear and hilbert schmidt bounded type are locally m convex frechet algebras we prove that the spectrum of these algebras has a natural analytic structure which we use to characterize the envelope of holomorphy we also show a cartan thullen type theorem

period distribution of generalized discrete arnold cat map for n p e in this paper we analyze the period distribution of the generalized discrete cat map over the galois ring where is a prime the sequences generated by this map are modeled as 2 dimensional lfsr sequences employing the generation function and the hensel lifting approaches full knowledge of the detail period distribution is obtained analytically our results not only characterize the period distribution of the cat map which gives insights to various applications but also demonstrate some approaches to deal with the period of a polynomial in the galois ring

atomic decompositions for tensor products and polynomial spaces abstract we study the existence of atomic decompositions for tensor products of banach spaces and spaces of homogeneous polynomials if a banach space x admits an atomic decomposition of a certain kind we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product s n x for any symmetric tensor norm in addition the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on x

modification rules for orthosymplectic superalgebras modification rules are presented for finite dimensional graded tensor representations of osp m n with the representations specified by young supertableaux these rules relate non standard supertableaux to standard supertableaux via the removal of continuous boundary hooks all typical tensor representations are treated together with atypical representations which satisfy up to two atypically conditions

the clebsch gordan coefficients and isoscalar factors of the graded unitary group su m n it is pointed out that the clebsch gordan coefficients cgc of the permutation group are the coefficients which couple irreducible bases irb of su m n and su p q to the irb of su mp nq mp np and the outer product reduction coefficients orc of the permutation group are the coefficients which couple the irb of su m n and su p q into the irb of su m p n q the orc of permutation groups with due modification in signs are the cgc for the special gel fand basis of su m n the isoscalar factor isf for the permutation group chain s f contains implies s f1 s f2 is the isf for the graded unitary group chain su mp nq mq np contains implies su m n su p q and the outer product isf for the group chain s f contains implies s f1 s f2 is the isf for su mp nq mq np contains implies su m n x su p q all these coefficients can be calculated easily and some are already available

unitary representations of non compact supergroups we give a general theory for the construction of oscillator like unitary irreducible representations uirs of non compact supergroups in a super fock space this construction applies to all non compact supergroupsg whose coset spaceg k with respect to their maximal compact subsupergroupk is hermitean supersymmetric we illustrate our method with the example of su m p n q by giving its oscillator like uirs in a particle state basis as well as supercoherent state basis the same class of uirs can also be realized over the super hilbert spaces of holomorphic functions of az variable labelling the coherent states

dynamics of non convolution operators and holomorphy types abstract in this article we study the hypercyclic behavior of non convolution operators defined on spaces of analytic functions of different holomorphy types over banach spaces the operators in the family we analyze are a composition of differentiation and composition operators and are extensions of operators in h c studied by aron and markose in 2004 the dynamics of this class of operators in the context of one and several complex variables was further investigated by many authors it turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear for example in contrast to the several complex variable case it may happen that the symbol of the composition operator has no fixed points and still the operator is not hypercyclic we also prove a runge type theorem for holomorphy types on banach spaces

superunitary reduction of the orthosymplectic supertableaux the supertableaux of the orthosymplectic groups osp 2 2p and osp 2 1 2p are decomposed in sums of supertableaux of the superunitary group su p

character expansions for the orthogonal and symplectic groups formulas for the expansion of arbitrary invariant group functions in terms of the characters for the sp 2n so 2n 1 and so 2n groups are derived using a combinatorial method the method is similar to one used by balantekin to expand group functions over the characters of the u n group all three expansions have been checked for all n by using them to calculate the known expansions of the generating function of the homogeneous symmetric functions an expansion of the exponential of the traces of group elements appearing in the finite volume gauge field partition functions is worked out for the orthogonal and symplectic groups

introduction to supersymmetric spin networks in this article we study the construction of supersymmetric spin networks which has a direct interpretation in context of the representation theory of the superalgebra in particular we analyze a special kind of spin network associated with superalgebra osp 1 2n it turns out that the set of corresponding spin network states forms an orthogonal basis of the hilbert space l2 a g and this argument holds even in the q deformed case the osp n 2 spin networks are also discussed briefly we expect they could provide useful techniques to quantum supergravity and gauge field theories from the point of nonperturbative view

irreducible representations of the superalgebras type ii the representation of the orthosymplectic algebras and the other members of their class are built explicitly with simple techniques

further result of compressing maps on primitive sequences modulo odd prime powers let be the integer residue ring with odd prime and integer for a sequence over there is an unique adic expansion where each is a sequence over and can be regarded as a sequence over the prime field gf naturally let be a strongly primitive polynomial over and the set of all primitive sequences generated by over suppose that gf gf it is shown that any function in is an injective map from to gf and the derived sequences of different functions are also different that is if and only if and for and these injective functions in can be considered as good candidates for the keys of a stream cipher

relation between the supertableaux of the supergroups osp 2 2 and su 1 2 the classification and the interpretation of the young supertableaux of the orthosymplectic group osp 2 2 are given a comparison is made with the supertableaux of the superunitary group su 1 2 taking advantage of the isomorphism of the corresponding superalgebras

further result on distribution properties of compressing sequences derived from primitive sequences over bf z p e let p be an odd prime number e an integer greater than 1 and z pe the integer residue ring modulo pe in this paper we obtain an improved result of the previous paper ieee trans inf theory 56 1 2010 555 563 on distribution properties of compressing sequences derived from primitive sequences over z pe it is shown that two primitive sequences and b generated by a strongly primitive polynomial f x over z pe are the same if there exist s z p and k z p such that the distribution of in their compressing sequences ae 1 a0 ae 2 and be 1 b0 be 2 is coincident at the positions t with t k where x0 xe 2 is an e variable polynomial over z p with the coefficient of xe 2p 1 x1p 1x0p 1 not equal to 1 e p 1 2 and is an m sequence over z p determined by f x and a compared with the previous result this gives a more precise characterization on the positions of a compressing sequence i e of the form ae 1 a0 ae 2 derived from a primitive sequence a over z pe that completely determines a in particular the result is also true for the highest level sequence ae 1 by taking x0 xe 2 0

geometry of integral polynomials m ideals and unique norm preserving extensions we use the aron berner extension to prove that the set of extreme points of the unit ball of the space of integral k homogeneous polynomials over a real banach space x is k x 1 with this description we show that for real banach spaces x and y if x is a nontrivial m ideal in y then ek sk sx the k th symmetric tensor product of x endowed with the injective symmetric tensor norm is never an m ideal in ek sk sy this result marks up a difference with the behavior of nonsymmetric tensors since when x is an m ideal in y it is known that ekkx the k th tensor product of x endowed with the injective tensor norm is an m ideal in ekky nevertheless if x is also asplund we prove that every integral k homogeneous polynomial in x has a unique extension to y that preserves the integral norm other applications to the metric and isomorphic theory of symmetric tensor products and polynomial ideals are also given

dimension and character formulas for lie supergroups a character formula is derived for lie supergroups the basic technique is that of symmetrization and antisymmetrization associated with young tableaux generalized to supergroups we rewrite the characters of the ordinary lie groups u n o n and sp 2n in terms of traces in the fundamental representation it is then shown that by simply replacing traces with supertraces the characters of certain representations for u n m and osp n 2m are obtained dimension formulas are derived by calculating the characters of a special diagonal supergroup element with 1 and 1 eigenvalues formulas for the eigenvalues of the quadratic casimir operators are given as applications the decomposition of a representation into representations of subgroups is discussed examples are given for the lie supergroup su 6 4 which has physical applications as a dynamical supersymmetry in nuclei

the casimir invariants and gel fand basis of the graded unitary group su m n in the space of f particle product states the casimir invariants of the graded unitary group su m n are functions of the class operators of the graded coordinate permutation group s f which are equal to the class operators of the graded state permutation group s f formulae for the quadratic and cubic casimir invariants are given it is shown that in general the eigenvalue formulae for the u m n casimir invariants as functions of the partition can be obtained from those for u m n by simply changing the argument of the functions from m n to m n the quasi standard basis of s f is identified with the gel fand basis of su m n i e the irreducible basis classified according to the group chain su m n contains implies su m n 1 contains implies su m contains implies su 2 contains implies u 1 the special gel fand basis of su m n for which the weight is restricted to 1 1 1 can be easily obtained from the gel fand basis of su m n with due allowances for modifying sign factors arising from the grading the construction of a general su m n gel fand basis is also discussed

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

diagram and superfield techniques in the classical superalgebras introduces the concept of graded permutation group in the analysis of tensor operators in the classical superalgebras for u m n and su m n irreducible tensor representations correspond to classes of young tableaux with definite graded symmetry type diagram techniques are given for kronecker products dimensions and branching rules the tensor techniques are complemented by the introduction of a superfluid formalism in which u m n and su m n act on polynomial functions over the appropriate superspace such superfluids may admit constraints a general superfield interpolates between the classes of young tableaux which correspond to particular types of constraint the tensor and superfield techniques are illustrated with case studies of su 2 1 and su m 1

two sided polynomial ideals on banach spaces abstract classes of homogeneous polynomials between banach spaces have been studied in the last three decades from the perspective of the stability with respect to the composition of a homogeneous polynomial with linear operators in an attempt to explore the underlying nonlinearity in a more consistent way and to bring the subject closer to its roots in complex analysis and also taking into account recent results in the field in this paper we propose the study of classes of homogeneous polynomials that are stable under the composition with homogeneous polynomials

hypercyclic convolution operators on frechet spaces of analytic functions a result of godefroy and shapiro states that the convolution operators on the space of entire functions on c n which are not multiples of identity are hypercyclic analogues of this result have appeared for some spaces of holomorphic functions on a banach space in this work we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators some known results come out as particular cases of this setting we also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the schatten von neumann class

hypercyclic subspaces for frechet space operators abstract a continuous linear operator t x x is hypercyclic if there is an x x such that the orbit t n x is dense and such a vector x is said to be hypercyclic for t recent progress show that it is possible to characterize banach space operators that have a hypercyclic subspace i e an infinite dimensional closed subspace h x of except for zero hypercyclic vectors the following is known to hold a banach space operator t has a hypercyclic subspace if there is a sequence n i and an infinite dimensional closed subspace e x such that t is hereditarily hypercyclic for n i and t n i 0 pointwise on e in this note we extend this result to the setting of frechet spaces that admit a continuous norm and study some applications for important function spaces as an application we also prove that any infinite dimensional separable frechet space with a continuous norm admits an operator with a hypercyclic subspace

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

further results on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers this paper studies the distinctness of primitive sequences over z m modulo 2 where m is an odd integer that is composite and square free and z m is the integer residue ring modulo m a new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f x over z m are pairwise distinct modulo 2 such result improves a recent result obtained in our previous paper and consequently the set of primitive sequences over z m that can be proven to be distinct modulo 2 is greatly enlarged

classification of finite dimensional unitary irreps for uq gl m n all finite dimensional irreducible unitary representations of the quantum supergroup uq gl m n are classified in terms of their highest weights for generic q 0

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

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

distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers let a and b be primitive sequences over z pe with odd prime p and e 2 for certain compressing maps we consider the distribution properties of compressing sequences of a and b and prove that a b if the compressing sequences are equal at the times t such that t k where is a sequence related to a we also discuss the s uniform distribution property of compressing sequences for some compressing maps we have that there exist different primitive sequences such that the compressing sequences are s uniform we also discuss that compressing sequences can be s uniform for how many elements s

spaces of σ p nuclear linear and multilinear operators on banach spaces and their duals abstract the theory of summing and nuclear linear operators on banach spaces was developed by pietsch 20 chapter 23 extending the linear case to the range p 1 and generalizing all cases to the multilinear setting in this paper we introduce the concept of p nuclear linear and multilinear operators in order to develop the duality theory for the spaces of such operators we introduce the concept of quasi p summing linear multilinear operators and prove pietsch type domination theorems for such operators the main result of the paper shows that under usual conditions linear functionals on the space of p nuclear n linear operators are represented via the borel transform by quasi p summing n linear operators as far as we know this result is new even in the linear case n 1

representations of the superalgebra f4 and young supertableaux the authors present a method for constructing typical as well as atypical finite dimensional representations of the superalgebra f4 for such a purpose young supertableaux are introduced

hook young diagrams with applications to combinatorics and to representations of lie superalgebras definition et etude des tableaux k l semi standards applications a la combinatoire et aux representations des superalgebres de lie des diagrammes de young a crochets