spectral parameter dependent approach to quantized algebra its multiparameter deformations and their q oscillator realizations yang baxterization of faddeev reshetikhin takhtajan algebra 1989 leading to quantum ybe is considered for a class of r matrices which satisfy hecke relations the authors apply such construction of the gl n case together with its multiparameter deformations revealing the connection between frt relations and the extended trigonometric sklyanin algebra new realizations of frt algebra through q oscillator modes are presented and their potential importance in the context of quantum integrable models is discussed a multiparametrized r matrix with the inclusion of spectral parameter is constructed as a by product

general topology optimization method with continuous and discrete orientation design using isoparametric projection a general topology optimization method which is capable of simultaneous design of density and orientation of anisotropic material is proposed by introducing orientation design variables in addition to the density design variable in this work the cartesian components of the orientation vector are utilized as the orientation design variables the proposed method supports continuous orientation design which is out of the scope of discrete material optimization approaches as well as design using discrete angle sets the advantage of this approach is that vector element representation is less likely to fail into local optima because it depends less on designs of former steps especially compared with using the angle as a design variable continuous fiber angle optimization by providing a flexible path from one angle to another with relaxation of orientation design space an additional advantage is that it is compatible with various projection or filtering methods such as sensitivity filters and density filters because it is free from unphysical bound or discontinuity such as the one at theta 2 pi and theta 0 seen with direct angle representation one complication of cartesian component representation is the point wise quadratic bound of the design variables that is each pair of element values has to reside in a given circular bound to overcome this issue we propose an isoparametric projection method which transforms box bounds into circular bounds by a coordinate transformation with isoparametric shape functions without having the singular point that is seen at the origin with polar coordinate representation a new topology optimization method is built by taking advantage of the aforementioned features and modern topology optimization techniques several numerical examples are provided to demonstrate its capability copyright c 2014 john wiley sons ltd

standard monomial theory for g2 let g be a semi simple algebraic group and b a borel subgroup let x be a schubert variety in g b let l be an ample line bundle on g b as well as its restriction to x a standard monomial theory for schubert varieties in g b is developed in 9 11 8 10 as a generalization of the classical hodge young theory cf 3 4 this theory consists in the construction of a characteristic free basis for h0 x l this theory is extended to schubert varieties in the infinite dimensional flag variety ln b in 13 see also 12 in this paper we extend the theory to schubert varieties in the infinite dimensional flag variety p2n b

penalty barrier multiplier methods for convex programming problems we study a class of methods for solving convex programs which are based on nonquadratic augmented lagrangians for which the penalty parameters are functions of the multipliers this gives rise to lagrangians which are nonlinear in the multipliers each augmented lagrangian is specified by a choice of a penalty function varphi and a penalty updating function pi the requirements on varphi are mild and allow for the inclusion of most of the previously suggested augmented lagrangians more importantly a new type of penalty barrier function having a logarithmic branch glued to a quadratic branch is introduced and used to construct an efficient algorithm convergence of the algorithms is proved for the case of pi being a sublinear function of the dual multipliers the algorithms are tested on large scale quadratically constrained problems arising in structural optimization

on resolving the multiplicity of the branching rule gl 2k 1 c down arrow so 2k 1 c we consider the multiplicity problem of the branching rule gl 2k 1 c down arrow so 2k 1 c finite dimensional irreducible representations of gl 2k 1 c are realized as right translations on subspaces of the holomorphic hilbert bargmann spaces of q 2k 1 complex variables maps are exhibited which carry an irreducible representation of so 2k 1 c into these subspaces an algebra of commuting operators is constructed eigenvalues and eigenvectors of certain of these operators can then be used to resolve the multiplicity in the branching rule

the universal r matrix and the yang baxter equation with parameters the authors formulate and demonstrate with some examples a method for obtaining solutions of the yang baxter equation with parameters

on resolving the multiplicity of tensor products of irreducible representations of symplectic groups the multiplicity problem of r fold tensor products of irreducible representations of sp 2k c are considered the arbitrary r fold tensor product is shown to be isomorphic to a subspace of the holomorphic hilbert bargmann space of n 2k complex variables maps are constructed which carry an irreducible representation of sp 2k c into this subspace an algebra of commuting operators is constructed and it is shown how eigenvalues and eigenvectors of certain of these operators can be used to resolve the multiplicity

exotic quantum double its universal r matrix and their representations the exotic quantum double and its universal r matrix for the quantum yang baxter equation are constructed in terms of drinfeld s quantum double theory as a new quasitriangular hopf algebra it is different from those standard quantum doubles that are the q deformations for lie algebras or lie superalgebras by studying its representation theory many parameter representations of the exotic quantum double are obtained with an explicit example associated with lie algebra a2 the multiparameter r matrices for the quantum yang baxter equation can result from the universal r matrix of this exotic quantum double and these representations

induction and restriction of kazhdan lusztig cells abstract barbasch and vogan gave a beautiful rule for restricting and inducing kazhdan lusztig representations of weyl groups in this paper we show that this rule implies and generalizes the littlewood richardson rule for decomposing outer products of representations of the symmetric groups a new recursive rule for computing characters of arbitrary coxeter groups follows another application is a generalization of garsia remmel s algorithm for decomposing certain tensor products of symmetric groups representations

modified barrier functions theory and methods the nonlinear rescaling principle employs monotone and sufficiently smooth functions to transform the constraints and or the objective function into an equivalent problem the classical lagrangian which has important properties on the primal and the dual spaces the application of the nonlinear rescaling principle to constrained optimization problems leads to a class of modified barrier functions mbf s and mbf methods mbfm s being classical lagrangians cl s for an equivalent problem the mbf s combine the best properties of the cl s and classical barrier functions cbf s but at the same time are free of their most essential deficiencies due to the excellent mbf properties new characteristics of the dual pair convex programming problems have been found and the duality theory for nonconvex constrained optimization has been developed the mbfm have up to a superlinear rate of convergence and are to the classical barrier functions cbf s method as the multipliers method for augmented lagrangians is to the classical penalty function method based on the dual theory associated with mbf the method for the simultaneous solution of the dual pair convex programming problems with up to quadratic rates of convergence have been developed the application of the mbf to linear lp and quadratic qp programming leads to a new type of multipliers methods which have a much better rate of convergence under lower computational complexity at each step as compared to the cbf methods the numerical realization of the mbfm leads to the newton modified barrier method nmbm the excellent mbf properties allow us to discover that for any nondegenerate constrained optimization problem there exists a hot start from which the nmbm has a better rate of convergence a better complexity bound and is more stable than the interior point methods which are based on the classical barrier functions

a finite element analysis of optimal variable thickness sheets a quasi mixed finite element fe method for maximum stiffness of variable thickness sheets is analyzed the displacement is approximated with nine node lagrange quadrilateral elements and the thickness is approximated as elementwise constant one is guaranteed that the fe displacement solutions will converge in hh but in an example it is shown that in general one cannot expect any subsequence of the fe thickness solutions to converge in any l p omega norm however under a regularity and biaxiality assumption on the optimal stress field uniqueness of the optimal thickness function as well as convergence in l p omega 1 leq p infty of fe thickness solutions are proven

trigonometric yang baxterization of coloured r matrix for a given coloured solution r lambda mu of the quantum yang baxter equation in appropriate form the authors present an explicit prescription to generate trigonometric solutions r lambda mu x of the yang baxter equation with spectral parameters x when the given r lambda mu admits the birman wenzl algebraic structure with colour they find that two types of the r lambda mu x are generated by such r lambda mu new explicit examples associated with the fundamental representations of an bn cn and dn are given in terms of this prescription

extended birman wenzl algebra and yang baxterization a new algebra a is presented by directly extending the birman wenzl algebra if a braid group representation with four distinct eigenvalues satisfies a then it can be yang baxterized to derive the solution of the yang baxter equation in terms of a standard scheme

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

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

generalized theta functions strange duality and odd orthogonal bundles on curves this paper studies spaces of generalized theta functions for odd orthogonal bundles with nontrivial stiefel whitney class and the associated space of twisted spin bundles in particular we prove a verlinde type formula and a dimension equality that was conjectured by oxbury wilson modifying hitchin s argument we also show that the bundle of generalized theta functions for twisted spin bundles over the moduli space of curves admits a flat projective connection we furthermore address the issue of strange duality for odd orthogonal bundles and we demonstrate that the naive conjecture fails in general a consequence of this is the reducibility of the projective representations of spin mapping class groups arising from the hitchin connection for these moduli spaces finally we answer a question of nakanishi tsuchiya about rank level duality for conformal blocks on the pointed projective line with spin weights

a note on graded yang baxter solutions as braid monoid invariants we construct two osp n mod 2m solutions of the graded yang baxter equation by using the algebraic braid monoid approach the factorizable s matrix interpretation of these solutions is also discussed

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 reciprocity law and the skew pieri rule for the symplectic group we use the theory of skew duality to show that decomposing the tensor product of k irreducible representations of the symplectic group sp2m sp2m is equivalent to branching from sp2n to sp2n1 sp2nk where n n1 nk are positive integers such that n n1 nk and the njs depend on m as well as the representations in the tensor product using this result and a work of lepowsky we obtain a skew pieri rule for sp2m i e a description of the irreducible decomposition of the tensor product of an irreducible representation of the symplectic group sp2m with a fundamental representation

optimal design of material properties and material distribution for multiple loading conditions an extension of recent work 1 on the simultaneous optimization of material and structure to address the design of structures under multiple loading conditions is presented material properties are represented in the most general form possible namely as elements of the unrestricted set of positive semi definite constitutive tensors of a linearly elastic continuum existence of solutions can be shown when the objective is a weighted average of compliances and a resource constraint measured as the 2 norm or the trace of the constitutive tensors is included the optimized material properties can be derived analytically the optimization of the layout of the material leads to a sizing problem of structural optimization involving a non linear non smooth elasticity analysis the computational solution of this problem is discussed and illustrated with examples

exactly solvable quantum spin ladders associated with the orthogonal and symplectic lie algebras we extend the results of spin ladder models associated with the lie algebras su 2 n to the case of the orthogonal and symplectic algebras o 2 n sp 2 n where n is the number of legs for the system two classes of models are found whose symmetry either orthogonal or symplectic has an explicit n dependence integrability of these models is shown for an arbitrary coupling of xx type rung interactions and applied magnetic field term

sections of homogeneous vector bundles abstract in this work we give a method for computing sections of homogeneous vector bundles on any rational homogeneous variety g p of type ade our main tool is the equivalence of categories between homogeneous vector bundles on g p and finite dimensional representations of a given quiver with relations our result generalizes the work of ottaviani and rubei 2006 or06

new solutions of yang baxter equations birman wenzl algebra and quantum group structures new braid group representations associated with the fundamental representations of bn cn and dn are derived they are shown to satisfy birman wenzl algebra by yang baxterization the authors obtain new solutions of yang baxter equations including the twisted extensions quantum group structures related to these new solutions are explicitly given

a non standard quantum double as the l state boson algebra and its r matrices for the quantum yang baxter equation in this paper we construct a new quantum double by endowing the l state boson algebra with a non trivial hopf algebra structure which is not a q deformation of the lie algebra or superalgebra the universal r matrix for the yang baxter equation associated with this new quantum group structure is obtained explicitly by building the representations of this quantum double we obtain some r matrices which can result in new representations of the braid group

bounds for decoupled design and analysis discretizations in topology optimization summary topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution this paper discusses the relation between the number of design variables per element and the order of the elements used for analysis we derive that beyond a maximum number of design variables certain sets of material distributions cannot be discriminated based on the corresponding analysis results this makes the design description inefficient and the solution of the optimization problem non unique to prevent this we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non uniqueness copyright 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

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

optimization of structure and material properties for solids composed of softening material an existing formulation for the prediction of the optimal material properties tensor for systems made of linear material is extended here to encompass design with nonlinear softening material the original model for the linear case was stated as a convex constrained nonlinear programming problem and this property is preserved in the extension the development is exemplified for the case of design for minimum global compliance an extremum problem formulation for elastostatics is incorporated into the design problem as a convenient way to model the structural analysis of general softening systems unlike the case for design with linear material in the nonlinear problem the form of the solution for optimal material properties and the associated stress fields as well evolve with increasing load computational results are presented for a two dimensional example problem in which a system is designed for different loads while parameters in the material model are held fixed

non birman wenzl algebraic properties and redundancy of exotic enhanced yang baxter operator for spin model in this paper we explicitly construct the markov trace for the general coloured exotic braid group representations bgr with spin j it is verified that the bgr for j 1 is redundant in the sense of murakami 1990 but no birman wenzl algebra

free material optimization with fundamental eigenfrequency constraints the goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure a natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable as an alternative we propose a new approach which is based on a nonlinear semidefinite low rank approximation of the semidefinite dual we introduce an algorithm based on this approach and analyze its convergence properties the article is concluded by numerical experiments proving the effectiveness of the new approach

free material design via semidefinite programming the multiload case with contact conditions free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can freely vary the case of one single load has been discussed in several recent papers and an efficient numerical approach was presented in m kovara m zibulevsky and j zowe rairo model math anal numer 32 1998 pp 255 281 we attack here the multiload situation understood in the worst case sense which is of much more interest for applications but also significantly more challenging from both the theoretical and the numerical points of view after a series of transformation steps we reach a problem formulation for which we can prove existence of a solution a suitable discretization leads to a semidefinite programming problem for which modern polynomial time algorithms of interior point type are available a number of numerical examples demonstrate the efficiency of our approach

truncated global transfer matrix trigonometric goryachev chaplygin gyrostat the rtt relation with truncation is solved for the r matrix associated with the six vertex model it turns out that the finite expansion of the global solution of the transfer matrix t u in terms of the spectral parameter u can be realized by the defined algebra formed by and the non commutative coordinates the hamiltonian of the system has been found which is the trigonometric deformation of the goryachev chaplygin gyrostat

r matrices of three state hamiltonians solvable by coordinate bethe ansatz we review some of the strategies that can be implemented to infer an r matrix from the knowledge of its hamiltonian we apply them to the classification achieved in crampe frappat and ragoucy j phys a 46 405001 2013 on three state u 1 invariant hamiltonians solvable by coordinate bethe ansatz focusing on models for which the s matrix is not trivial for the 19 vertex solutions we recover the r matrices of the well known zamolodchikov fateev and izergin korepin models we point out that the generalized bariev hamiltonian is related to both main and special branches studied by martins in nucl phys b 874 243 2013 that we prove to generate the same hamiltonian the 19 vertex spr model still resists to the analysis although we are able to state some no go theorems on its r matrix for 17 vertex hamiltonians we produce a new r matrix

stability of finite element models for distributed parameter optimization and topology design abstract we address a problem of numerical instability that is often encountered in finite element solutions of distributed parameter optimization and variable topology shape design problems we show that the cause of this problem is numerical rather than physical in nature we consider a two field distributed parameter optimization problem involving a design field and a response field and show that the optimization problem corresponds to a mixed variational problem an improper selection of the discrete function spaces for these two fields leads to grid scale anomalies in the numerical solutions to optimization problems similar to those that are sometimes encountered in mixed formulations of the stokes problem we present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models the general theoretical framework is specialized to analyze the stability of specific optimization problems and stability results for various mixed finite element models are presented we propose patch tests that are useful in identifying unstable elements

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

material optimization in transverse electromagnetic scattering applications a class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed the idea behind the algorithm is similar to that of the sequential programming however in each major iteration a model is established on the basis of an appropriately parametrized material tensor the resulting nonlinear parametrization is treated on the level of the subproblem for which globally optimal solutions can be computed due to the block separability of the model although global optimization of nonconvex design problems is generally prohibitive a well chosen combination of analytic solutions along with standard global optimization techniques leads to a very efficient algorithm for most relevant material parametrizations a global convergence result for the overall algorithm is established the effectiveness of the approach in terms of both computation time and solution quality is demonstrated by numerical examples based on a two dimensional helmholtz equation inclu

isomorphism of two realizations of quantum affine algebra u_q widehat mathfrak g mathfrak l text n text we establish an explicit isomorphism between two realizations of the quantum affine algebra u q widehat mathfrak g mathfrak l text n text given previously by drinfeld and reshetikhin semenov tian shansky our result can be considered as an affine version of the isomorphism between the drinfield jimbo and the faddeev reshetikhin takhtajan constructions of the quantum algebra u q mathfrak g mathfrak l n

exactly soluble isotropic spin ladder models the undeformed limit of the dilute two colour braid monoid algebra gives a natural basis for the description of spin ladder models and allows different baxterization ansatze based on this observation we find the complete classification of exactly soluble generalized isotropic spin ladder models

integrable boundary conditions for multi species asep the first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi species asep with anarbitrary number of species all the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary hecke algebra the boundary hecke algebra isnot sufficient to build these solutions this is the second result of ourpaper

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

free material optimization via mathematical programming this paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied we consider a general multi load formulation and include the possibility of unilateral contact the emphasis of the presentation is on numerical procedures for this type of problem and we show that the problems after discretization can be rewritten as mathematical programming problems of special form we propose iterative optimization algorithms based on penalty barrier methods and interior point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach

quivers and the cohomology of homogeneous vector bundles we describe the cohomology groups of a homogeneous vector bundle e on any hermitian symmetric variety x g p of ade type as the cohomology of a complex explicitly described the main tool is the equivalence introduced by bondal kapranov and hille between the category of homogeneous bundles and the category of representations of a certain quiver qx with relations we prove that the relations are the commutative ones on projective spaces but they involve additional scalars on general grassmannians in addition we introduce moduli spaces of homogeneous

a recursive rule for kazhdan lusztig characters abstract a formula for computing kazhdan lusztig characters in hecke algebras of coxeter groups is given this formula holds for products of coxeter elements of parabolic subgroups in an arbitrary coxeter group where the parabolic subgroups are of type a and the kazhdan lusztig representations are of finite dimension the formula yields new combinatorial interpretations of murnaghan nakayama type to these characters and to other related characters

bethe subalgebras in affine birman murakami wenzl algebras and flat connections for q kz equations commutative sets of jucys murphy elements for affine braid groups of types were defined construction of r matrix representations of the affine braid group of type and its distinguished commutative subgroup generated by the type jucys murphy elements are given we describe a general method to produce flat connections for the two boundary quantum knizhnik zamolodchikov equations as necessary conditions for sklyanin s type transfer matrix associated with the two boundary multicomponent zamolodchikov algebra to be invariant under the action of the type jucys murphy elements we specify our general construction to the case of the birman murakami wenzl algebras bmw algebras for short as an application we suggest a baxterization of the dunkl cherednik elements in the double affine hecke algebra of type a

universal baxterization for z graded hopf algebras we present a method for baxterizing solutions of the constant yang baxter equation associated with z graded hopf algebras to demonstrate the approach we provide examples for the taft algebras and the quantum group u q sl 2

on character generators for simple lie algebras we study character generating functions character generators of simple lie algebras the expression due to patera and sharp derived from the weyl character formula is first reviewed a new general formula is then found it makes clear the distinct roles of outside and inside elements of the integrity basis and helps determine their quadratic incompatibilities we review analyse and extend the results obtained by gaskell using the demazure character formulae we find that the fundamental generalized poset graphs underlying the character generators can be deduced from such calculations these graphs introduced by baclawski and towber can be simplified for the purposes of constructing the character generator the generating functions can be written easily using the simplified graphs and associated demazure expressions the rank two algebras are treated in detail but we believe our results are indicative of those for general simple lie algebras

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

a new braid like algebra for baxterisation we introduce a new baxterisation for r matrices that depend separately on two spectral parameters the baxterisation is based on a new algebra close to but different from the braid group we study representations of this new algebra on the vector space mathbb c m otimes n when the generators act locally the ones for m 2 are completely classified we also introduce some representations for generic m they allow us to recover the r matrix of the multi species generalization of the totally asymmetric simple exclusion process with different hopping rates

identities for classical group characters of nearly rectangular shape abstract we derive several identities that feature irreducible characters of the general linear the symplectic the orthogonal and the special orthogonal groups all of the identities feature characters that are indexed by shapes that are nearly rectangular by which we mean that the shapes are rectangles except for one row or column that might be shorter than the others as applications we prove new results in plane partitions and tableaux enumeration including new refinements of the bender knuth and macmahon ex conjectures

universal spectral parameter dependent lax operators for the drinfeld double of the dihedral group d3 two universal spectral parameter dependent lax operators are presented in terms of the elements of the drinfeld double d d3 of the dihedral group d3 applying representations of d d3 to these yields matrix solutions of the yang baxter equation with a spectral parameter

multidisciplinary free material optimization we present a mathematical framework for the so called multidisciplinary free material optimization mdfmo problems a branch of structural optimization in which the full material tensor is considered as a design variable we extend the original problem statement by a class of generic constraints depending either on the design or on the state variables among the examples are local stress or displacement constraints we show the existence of optimal solutions for this generalized free material optimization fmo problem and discuss convergent approximation schemes based on the finite element method

equivalent isotropic osp 2 2 spin chains and its bethe ansatz analysis in this paper we discuss the equivalence between two integrable and isotropic osp 2 2 chains via the braid monoid approach we use the analytical bethe ansatz approach in order to solve the spectrum of these systems the ground state is parametrized by a special structure of the bethe ansatz roots their interpretation in terms of correlated fermionic models is briefly discussed

tensor products of representations if g is a reductive group in characteristic zero with two irreducible representations v1 and v2 we may form the tensor product representation v1 0 v2 where g acts diagonally the problem is to decompose v1 0 v2 into its irreducible components with their multiplicities of course this may be done using weyl s character formula but this is a very difficult calculation this paper presents a general method for doing this calculation in a more efficient way for the general linear group the method was explained in 2 with a minimum of group theoretic language for the other classical groups this paper will give explicit formulas the method of this paper may be used for exceptional groups but for combinatorial reasons it does not seem worthwhile at this point to write an explicit formula perhaps it would be more useful to have a computer program for the calculation as an after thought i have included an appendix on how to decompose an irreducible representation of g when restricted to a large reductive subgroup the case of the general linear group is well known