supergeneralization of duffin kemmer petiau algebra and lie superalgebra osp n m we will consider a supergeneralization of the duffin kemmer petiau algebra it has been shown to be intimately related to the lie super algebra osp n m we will also discuss its representations

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

longest property preserved common factor a new string processing framework abstract we introduce a new family of string processing problems given two or more strings we are asked to compute a factor common to all strings that preserves a specific property and has maximal length we consider three fundamental string properties square free factors periodic factors and palindromic factors under three different settings one per property in the first setting we are given a string x and we are asked to construct a data structure over x answering the following type of online queries given a string y find a longest square free factor common to x and y in the second setting we are given k strings and an integer 1 k k and we are asked to find a longest periodic factor common to at least k strings in the third one we are given two strings and we are asked to find a longest palindromic factor common to the two strings we present linear time solutions for all settings this is a full and extended version of a paper from spire 2018

holomorphic extensions in complex fiber bundles abstract the main result of this paper is the existence of solutions of the equation u for closed 0 1 forms with compact support in a complex fiber bundle from some class this class of bundles contains for example vector bundles what is important the solution exists for any base manifold the solvability property implies many results about extension and representation of complex analytic and cauchy riemann functions riemann hilbert type representation hartogs and hartogs bochner phenomena vanishing of some cohomology groups to mention few

lie superalgebras and the multiplet structure of the genetic code i codon representations it has been proposed by hornos and hornos phys rev lett 71 4401 4404 1993 that the degeneracy of the genetic code i e the phenomenon that different codons base triplets of dna are transcribed into the same amino acid may be interpreted as the result of a symmetry breaking process in their work this picture was developed in the framework of simple lie algebras here we explore the possibility of explaining the degeneracy of the genetic code using basic classical lie superalgebras whose representation theory is sufficiently well understood at least as far as typical representations are concerned in the present paper we give the complete list of all typical codon representations typical 64 dimensional irreducible representations whereas in the second part we shall present the corresponding branching rules and discuss which of them reproduce the multiplet structure of the genetic code

on wedge extendability of cr meromorphic functions in this article we consider metrically thin singularities e of the solutions of the tangential cauchy riemann operators on a mathcal c 2 alpha smooth embedded cauchy riemann generic manifold m cr functions on m backslash e and more generally we consider holomorphic functions defined in wedgelike domains attached to m backslash e our main result establishes the wedge and the l1 removability of e under the hypothesis that the dim m 2 dimensional hausdorff volume of e is zero and that m and m backslash e are globally minimal as an application we deduce that there exists a wedgelike domain attached to an everywhere locally minimal m to which every cr meromorphic function on m extends meromorphically

the hartogs type extension theorem for meromorphic maps into compact kahler manifolds extension theorems of this type are often called hartogs type extension theorems the above result was conjectured by griffiths see problem 1 in gr who proved it in the special case when d p o i n t and f d x is holomorphic important contributions towards the proof of this conjecture were made by b shiffman y t siu n sibony see sh sil sb3 in particular y t siu proved a thullen type extension theorem for meromorphic maps into compact kfihler manifolds see w 1 the above theorem can be applied to the study of covering maps of zariski open subsets in compact kfihler manifolds recall that a subdomain d of a complex manifold m is called levi pseudoconvex if for any peod there exists a neighbourhood u of p in m such that u c d is stein we say that d covers a complex manifold x if there is a subgroup g c aut d acting properly discontinuously and freely on d with d g x

deformation of orthosymplectic lie superalgebra osp 1 4 triangular deformation of the orthosymplectic lie superalgebra osp 14 is defined by chains of twists the corresponding classical r matrix is obtained by a contraction procedure from the trigonometric r matrix the carrier space of the constant r matrix and the twist element is the borel subalgebra the known super jordanian twist of osp 12 is generalized as an extended twist to the orthosymplectic lie superalgebras of higher rank the dimension of the cobracket kernel is related to the number of generators with primitive twisted coproduct of the deformed algebra

on casimir s ghost we define on the universal enveloping superalgebra of a nonstandard adjoint action endowing it with a module structure this allows in particular to construct a bosonic operator which anticommutes with all the fermionic generators and which appears to be the square root of a certain casimir operator

an example concerning extension and separate analyticity properties of meromorphic mappings we construct a compact complex manifold x of dimension three such that every meromorphic map from a two dimensional domain into x extends meromorphically onto the envelope of holomorphy of this domain but there exists a meromorphic map from the punctured three dimensional ball into x which does not extend to the origin we give a theorem describing the obstructions occuring here

motif trie an efficient text index for pattern discovery with don t cares abstract we introduce the motif trie data structure which has applications in pattern matching and discovery in genomic analysis plagiarism detection data mining intrusion detection spam fighting and time series analysis to name a few here the extraction of recurring patterns in sequential and textual data is one of the main computational bottlenecks for this we address the problem of extracting maximal patterns with at most k don t care symbols and at least q occurrences according to a maximality notion we define we apply the motif trie to this problem also showing how to build it efficiently as a result we give the first algorithm that attains a stronger notion of output sensitivity where the cost for an input sequence of n symbols is proportional to the actual number of occurrences of each pattern which is at most n much smaller in practice this avoids the best known cost of o n c per pattern for constant c 1 which is otherwise impractical for massive sequences with large n

symmetrizable quantum affine superalgebras and their representations aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable cartan matrices are studied the irreducible integrable highest weight representations are classified and shown to be deformations of their classical counterparts it is also shown that jimbo type quantum affine superalgebras can be obtained by deforming universal enveloping algebras of ordinary i e nongraded affine algebras supplemented by certain parity operators

irredundant tandem motifs eliminating the possible redundancy from a set of candidate motifs occurring in an input string is fundamental in many applications the existing techniques proposed to extract irredundant motifs are not suitable when the motifs to search for are structured i e they are made of two or several subwords that co occur in a text string s of length n the main effort of this work is studying and characterizing a compact class of tandem motifs that is pairs of substrings occurring in tandem within a maximum distance of d symbols in s where d is an integer constant given in input to this aim we first introduce the concept of maximality related to four specific conditions that hold only for this class of motifs then we eliminate the remaining redundancy by defining the notion of irredundancy for tandem motifs we prove that the number of non overlapping irredundant tandem motifs is o d 2n which considering d as a constant leads to a linear number of tandems in the length of the input string this is an order of magnitude less than previously developed compact indexes for tandem extraction the notions and bounds provided for tandem motifs are generalized for the case r 2 if r is the number of subwords composing the motifs finally we also provide an algorithm to extract irredundant tandem motifs

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

suffix tree characterization of maximal motifs in biological sequences finding motifs in biological sequences is one of the most intriguing problems for string algorithm designers due to on the one hand the numerous applications of this problem in molecular biology and on the other hand the challenging aspects of the computational problem indeed when dealing with biological sequences it is necessary to work with approximations that is to identify fragments that are not necessarily identical but just similar according to a given similarity notion and this complicates the problem existing algorithms run in time linear with respect to the input size nevertheless the output size can be very large due to the approximation namely exponential in the approximation degree this often makes the output unreadable as well as slowing down the inference itself a high degree of redundancy has been detected in the set of motifs that satisfy traditional requirements even for exact motifs moreover it has been observed many times that only a subset of these motifs namely the maximal motifs could be enough to provide the information of all of them in this paper we aim at removing such redundancy we extend some notions of maximality already defined for exact motifs to the case of approximate motifs with hamming distance and we give a characterization of maximal motifs on the suffix tree given that this data structure is used by a whole class of motif extraction tools we show how these tools can be modified to include the maximality requirement without changing the asymptotical complexity

schottky groups acting on homogeneous rational manifolds we systematically study schottky group actions on homogeneous rational manifolds and find two new families besides those given by nori s well known construction this yields new examples of non k ahler compact complex manifolds having free fundamental groups we then investigate their analytic and geometric invariants such as the kodaira and algebraic dimension the picard group and the deformation theory thus extending results due to l arusson and to seade and verjovsky as a byproduct we see that the schottky construction allows to recover examples of equivariant compactifications of sl 2 c gamma for gamma a discrete free loxodromic subgroup of sl 2 c previously obtained by a guillot

eigenvalues of casimir operators for the general linear the special linear and the orthosymplectic lie superalgebras the generators of the algebras under consideration can be written in a canonical two index form and hence the associated standard sequence of casimir elements can be constructed following the classical approach by perelomov and popov we obtain the eigenvalues of these casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions

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

basic hypergeometric functions and covariant spaces for even dimensional representations of uq osp 1 2 representations of the quantum superalgebra uq osp 1 2 and their relations to the basic hypergeometric functions are investigated we first establish clebsch gordan decomposition for the superalgebra uq osp 1 2 in which the representations having no classical counterparts are incorporated formulae for these clebsch gordan coefficients are derived and is observed that they may be expressed in terms of the q hahn polynomials we next investigate representations of the quantum supergroup ospq 1 2 which are not well defined in the classical limit employing the universal matrix the representation matrices are obtained explicitly and found to be related to the little q jacobi polynomials characteristically the relation q q is satisfied in all cases using the clebsch gordan coefficients derived here we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup ospq 1 2

jacobson generators fock representations and statistics of sl n 1 the properties of a statistics related to the class a of simple lie algebras t d palev preprint jinr e17 10550 1977 hep th 9705032 are further investigated the description of each sl n 1 is carried out via generators a1 an which we call jacobson generators with respect to these generators the definition of a fock space of sl n 1 is given it is proved that the fock spaces wp p n are the simple symmetric finite dimensional modules of sl n 1 the pauli principle of the underlying statistics is formulated within each wp operators b p i ai p i 1 n called quasi bose creation and annihilation operators caos are defined then limp b p i bi where bi are ordinary bose caos therefore a statistics appears as an approximation of bose statistics with caos acting in finite dimensional state spaces we indicate that the p 1 quasi bose operators b 1 1 b 1 n are natural operators for the description of hard core bose models and of the related heisenberg spin models we argue th

a remarkable connection between the representations of the lie superalgebras osp 1 2n and the lie algebras o 2n 1 we show that there is a one to one correspondence between the graded representations of osp 1 2n and the non spinorial representations of o 2n 1 the clebsch gordan series for osp 1 2n reduce to the corresponding series for o 2n 1 and the properly defined casimir operators of order at least up to four have the same eigenvalues