an inverse eigenvalue problem for jacobi matrix the paper considers an inverse eigenvalue problem of jacobi matrix which is obtained from reconstruction of a fixed free mass spring system of size 2 n from its spectrum and from existing physical parameters of the first half of the particles the necessary and sufficient conditions for the solvability of the problem are derived two numerical algorithms and some numerical examples are given

irreducible representations of yangians abstract we give explicit realizations of irreducible representations of the yangian of the general linear lie algebra and of its twisted analogues corresponding to symplectic and orthogonal lie algebras in particular we develop the fusion procedure for twisted yangians for the non twisted yangian this procedure goes back to the works of cherednik

dual hybrid trefftz element formulation based on independent boundary traction frame reference epfl article 102727view record in web of science record created on 2007 04 23 modified on 2016 08 08

generalized bell states and principal realization of the yangian y sln we prove that the action of the yangian algebra y sln is better described by the principal generators on the tensor product of the fundamental representation and its dual the generalized bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product under the yangian symmetry the new quantum number j2 is also explicitly computed which gives an explanation for these maximally entangled states

the presentation and q deformation of special linear lie superalgebras it is shown that the naive serre presentation corresponding to the simplest cartan matrix of the special linear lie superalgebra sl m n yields for m n 2 a larger lie superalgebra s m n of which sl m n is a nontrivial quotient the missing relations are found and the q deformation of the universal enveloping algebra of sl m n is constructed some auxiliary results related to associative algebras and e lie algebras defined in terms of generators and relations are also included

r matrices and the magic square the distinguished representations associated with the rows of the freudenthal magic square have a uniform tensor product graph with edges labelled by linear functions of the dimension of the corresponding division algebra

rational k matrices and representations of twisted yangians we describe the twisted yangians y g h which arise as boundary remnants of yangians y g in 1 1d integrable field theories we describe and extend our recent construction of the intertwiners of their representations the rational boundary s or k matrices and perform a case by case analysis for all pairs g h giving the h decomposition of y g h representations where possible

an r matrix for d 3 4 this letter gives the calculation of a trigonometric r matrix for the twisted affine quantum group of type d 3 4

constructing jacobi matrices with prescribed ordered defective eigenpairs and a principal submatrix this paper considers the problem of constructing a jacobi matrix from prescribed ordered defective eigenpairs and the leading principal submatrix according to the relationship between the eigenvalue ordered and the number of variations in signs of the corresponding eigenvector the necessary and sufficient conditions for the solvability of the problem are derived and the numerical algorithm is developed numerical examples show that the algorithm is quite efficient

the trigonometric casimir connection of a simple lie algebra abstract let g be a complex semisimple lie algebra g the corresponding simply connected lie group and h g a maximal torus we construct a flat connection on h with logarithmic singularities on the root hypertori and values in the yangian y g of g by analogy with the rational casimir connection of g we conjecture that the monodromy of this trigonometric connection is described by the quantum weyl group operators of the quantum loop algebra u l g

connection between yangian symmetry and the quantum inverse scattering method the quantum nonlinear schrodinger model with two component fermions exhibits a yangian symmetry when considered on an infinite interval we construct the generators of the yangian using dunkl operators we show an equivalence between the monodromy matrix constructed from the dunkl operators and that of the quantum inverse scattering method under the yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations

the algebraic structure of the gl n m color calogero sutherland models we extend the study on the algebraic structure of the su n color calogero sutherland cs models to the case of gl n m color cs model and show that the generators of the super yangian y gl n m can be obtained from two gl n m loop algebras also a super w infinity algebra for the susy cs model is constructed c 1998 american institute of physics

bosonic representations of yangian double with on the basis of the rtt ttr formalism we introduce the quantum double of the yangian for with a central extension the gauss decomposition of the t matrices gives us the so called drinfel d generators using these generators we present some examples of both finite and infinite dimensional representations that are quite natural deformations of their corresponding affine counterpart

staggered polarization of vertex models with u_q widehat sl n symmetry in this paper we give an explicit formula for level 1 vertex operators related to u q widehat sl n as operators on the fock spaces we derive also their commutation relations as an application we calculate with the vector representation of u q widehat sl n thereby extending the recent work on the staggered polarization of the xxz model

free boson representation of dyℏ gln k and dyℏ sln k we construct a realization of the yangian double dy h over bar gl n k and dy h over bar sl n k for an arbitrary level k in terms of free boson fields with a continuous parameter in the h over bar 0 limit this realization becomes the wakimoto realization of affine lie algebras gl n and sl n respectively the vertex operators and the screening currents are also constructed with the same spirits the screening currents commute with dy h over bar sl n module total difference c 1998 american institute of physics s0022 2488 98 00104 2

the submatrix constraint problem of matrix equation axb cyd e we say that x x i j i j 1 n is symmetric centrosymmetric if x i j x j i and x n j 1 n i 1 1

free field representation for massive integrable models a new approach to massive integrable models is considered it allows one to find symmetry algebras which define the spaces of local operators and to get general integral representations for form factors in thesu 2 thirring and sine gordon models

a kind of inverse eigenvalue problems of jacobi matrix this paper considers the problem of constructing two jacobi matrices from their principal submatrix and specially ordered defective eigenpairs the two jacobi matrices are the same except for the entries in the last column and last row the necessary and sufficient condition of solvability is derived furthermore two algorithms and numerical examples are given

the elliptic quantum algebra aq p sln and its bosonization at level one we extend the work of foda et al and propose an elliptic quantum algebra aq p sln similar to the case of aq p sl2 our presentation of the algebra is based on the relation rll llr where r and r are zn symmetric r matrices with the elliptic moduli chosen differently and a scalar factor is also involved with the help of the results obtained by asai et al we realize type i and type ii vertex operators in terms of bosonic free fields for the zn symmetric belavin model we also give a bosonization for the elliptic quantum algebra aq p sln at level one

the hybrid trefftz finite element model and its application to plate bending this paper presents a new hybrid element approach and applies it to plate bending in contrast to more conventional models the formulation is based on displacement fields which fulfil a priori the non homogeneous lagrange equation trefftz method the interelement continuity is enforced by using a stationary principle together with an independent interelement displacement the final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs the formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve sided elements to be generated where relevant known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain for example particular singular corner elements elements presenting circular holes etc thus a high degree of accuracy may be achieved without a troublesome mesh refinement another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements triangles quadrilaterals etc presenting an increasing degree of accuracy the paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements the conclusions present some ideas concerning the adaptive version of the new elements extension to nonlinear problems and some other developments

isomorphism between the r matrix and drinfeld presentations of yangian in types b c and d it is well known that the gauss decomposition of the generator matrix in the r matrix presentation of the yangian in type a yields generators of its drinfeld presentation defining relations between these generators are known in an explicit form thus providing an isomorphism between the presentations it has been an open problem since the pioneering work of drinfeld to extend this result to the remaining types we give a solution for the classical types b c and d by constructing an explicit isomorphism between the r matrix and drinfeld presentations of the yangian it is based on an embedding theorem which allows us to consider the yangian of rank n 1 as a subalgebra of the yangian of rank n of the same type

gauss decomposition of the yangian y mathfrak gl _ m n we describe a gauss decomposition for the yangian y mathfrak gl m n of the general linear lie superalgebra this gives a connection between this yangian and the yangian of the classical lie superalgebra y a m 1 n 1 for m n defined and studied in papers by stukopin and suggests natural definitions for the yangians y mathfrak sl n n and y a n n we also show that the coefficients of the quantum berezinian generate the centre of the yangian y mathfrak gl m n this was conjectured by nazarov in 1991

rational representations of yangians associated with skew young diagrams consider the general linear group gl m over the complex field the irreducible rational representations of the group gl m can be labeled by the pairs of partitions and such that the total number of non zero parts of and does not exceed m let eq4 be the irreducible representation corresponding to such a pair regard the direct product as a subgroup of gl n m take any irreducible rational representation of gl n m the vector space comes with a natural action of the group gl n put n for any pair of standard young tableaux of skew shapes respectively we give a realization of as a subspace in the tensor product of n copies of defining representation of gl n and of n copies of the contragredient representation this subspace is determined as the image of a certain linear operator on w nnn we introduce this operator by an explicit multiplicative formula when m 0 and is an irreducible representation of gl n we recover the known realization of as a certain subspace in the space of all traceless tensors in then the operator may be regarded as the rational analogue of the young symmetrizer corresponding to the tableau of shape even when m 0 our formula for is new our results are applications of the representation theory of the yangian of the lie algebra in particular is an intertwining operator between certain representations of the algebra on we also introduce the notion of a rational representation of the yangian as a representation of the image of is rational and irreducible

on the vertex operators of the elliptic quantum algebra uq p sl2 k a realization of the elliptic quantum algebra uq p sl2 for any given level k is constructed in terms of three free boson fields and their accompanying twisted partners it can be viewed as the elliptic deformation of the wakimoto realization two screening currents are constructed they commute or anticommute with uq p sl2 modulo total q differences the free field realization for two types of vertex operators nominated as the type i and the type ii vertex operators is presented the twisted version of the two types of vertex operators are also obtained they all play crucial roles in calculating correlation functions

an embedded strong discontinuity model for cracking of plain concrete abstract a numerical model formulated within the framework of a nonsymmetric strong discontinuity approach for fracture simulations of plain concrete is presented the model is based on the fixed crack concept and makes use of the concept of the elements with embedded discontinuities discontinuity segments of individual elements are considered to form a c0 continuous path enforcement of continuity of the crack path across adjacent elements is established by a partial domain crack tracking algorithm orientation of individual crack segments is derived from a nonlocal strain field the capabilities of the model are shown by means of numerical examples

local weyl modules and cyclicity of tensor products for yangians let mathfrak g be the exceptional complex simple lie algebra of type g2 we provide a concrete cyclicity condition for the tensor product of fundamental representations of the yangian y mathfrak g using this condition we show that every local weyl module is isomorphic to an ordered tensor product of fundamental representations of y mathfrak g

the elliptic quantum algebra u_ q hbox scriptsize p widehat sl_n and its vertex operators we construct a realization of the elliptic quantum algebra for any given level k in terms of free boson fields and their twisted partners it can be considered as the elliptic deformation of the wakimoto realization of the quantum affine algebra we also construct a family of screening currents which commute with the currents of up to total q differences and we give explicit twisted expressions for the type i and type ii vertex operators of by twisting the known results of the type i vertex operators of the quantum affine algebra and the new results of the type ii vertex operators of we obtained in this paper

partial gauss decomposition and zamolodchikov algebra we use the idea of partial gauss decomposition to study structures related to inside this gives a description of as an extension of with zamolodchikov algebras we describe the connection of this new realization with form factors

finite dimensional irreducible representations of twisted yangians we study quantized enveloping algebras called twisted yangians they are analogs of the yangian y gl n for the classical lie algebras of b c and d series the twisted yangians are subalgebras in y gl n and coideals with respect to the coproduct in y gl n we give a complete description of their finite dimensional irreducible representations every such representation is highest weight and we give necessary and sufficient conditions for an irreducible highest weight representation to be finite dimensional the result is analogous to drinfeld s theorem for the ordinary yangians its detailed proof for the a series is also reproduced for the simplest twisted yangians we construct an explicit realization for each finite dimensional irreducible representation in tensor products of representations of the corresponding lie algebras

representations of super yangian the classification of the finite dimensional irreducible representations of the super yangian associated with the lie superalgebra gl 1 1 is presented in detail

isomorphism between two realizations of the yangian y mathfrak so _3 the isomorphism between drinfeld s new realization and the frt realization is proved for the yangian algebra using gauss decomposition

physical parameters reconstruction of a fixed fixed mass spring system from its characteristic data in this paper an inverse problem of constructing a linear n degree of freedom mass spring system from part of its physical parameters and part of modality of its maximal or minimal natural frequencies is considered the solvability and the expression of the solution is derived the numerical algorithms and some numerical examples are given

parabolic presentations of the yangian we introduce some new presentations for the yangian associated to the lie algebra open image in new window these presentations are parametrized by tuples of positive integers summing to n at one extreme for the tuple n the presentation is the usual rtt presentation of y n at the other extreme for the tuple 1 n the presentation is closely related to drinfeld s presentation in general the presentations are useful for understanding the structure of the standard parabolic subalgebras of y n

an application of trefftz method to the sensitivity analysis of two dimensional potential problem this paper presents a new formulation for the sensitivity analysis with the help of the trefftz boundary type solution procedure direct differentiation of the expressions of the field variables leads to the expressions of the sensitivities since the field variables are approximated by linear combination of regular t complete functions the analytical expressions of the sensitivities are also regular sensitivity analysis schemes with respect to variations of dimensions of the object and boundary conditions are explained in detail two dimensional potential problems in the bounded region are considered as a numerical example in order to confirm its validity

on shifted super yangians and a class of finite w superalgebras abstract let e be an even nilpotent element satisfying certain restrictions on its jordan type in a general linear lie superalgebra we study the finite w superalgebra w e associated to such an e and a realization of w e in terms of a quotient of a shifted super yangian is established

super yangian double dy gl 1 1 and its gauss decomposition we extend the yangian double to the super or graded case and give its drinfel d generators a realization by gauss decomposition

towards a cladistics of double yangians and elliptic algebras a self contained description of algebraic structures obtained by combinations of various limit procedures applied to vertex and face sl 2 elliptic quantum affine algebras is given new double yangian structures of dynamical type are defined connections between these structures are established a number of them take the form of twist like actions these are conjectured to be evaluations of universal twists

shifted yangians and finite w algebras we give a presentation for the finite w algebra associated to a nilpotent matrix in the general linear lie algebra over c in the special case that the nilpotent matrix consists of n jordan blocks each of the same size l the presentation is that of the yangian of level l associated to gln as was first observed by ragoucy and sorba in the general case we are lead to introduce some generalizations of the yangian which we call the shifted yangians

the expansion problem of anti symmetric matrix under a linear constraint and the optimal approximation this paper mainly discusses the following two problems problem i given a rn m b rm m x0 asrq q the set of q q anti symmetric matrices find x asrn n such that atxa b x0 x 1 q where x 1 q is the q q leading principal submatrix of matrix x problem ii given x rn n find x se such that x x minx se x x where is the frobenius norm and se is the solution set of problem i the necessary and sufficient conditions for the existence of and the expressions for the general solutions of problem i are given moreover the optimal approximation solution an algorithm and a numerical example of problem ii are provided

an inverse extreme eigenpair problem and its parallel iterative solution for symmetric tridiagonal matrices this article concerns computing the largest or smallest eigenvalue and corresponding eigenvector of a large irreducible symmetric tridiagonal matrix we divide the original extreme eigenpair problem into p subproblems when the matrix is partitioned in p block form an inverse extreme eigenpair problem associated with the divide method is considered find a p 1 dimensional vector a such that the largest eigenvalue lambda of a given symmetric tridiagonal matrix t is the common largest eigenvalues of p small matrices t i a which are updated matrices of the diagonal blocks t i of t with rank one two corrections we prove that the inverse problem is solvable and has a unique positive solution and that the corresponding eigenvector of t i a with the positive solution a forms a section of the eigenvector of t corresponding to its largest eigenvalue an algorithm is proposed for solving the inverse problem iteratively on which a system of nonlinear equations should be solved for each of it

the full set of cn invariant factorized s matrices the author uses the method of the tensor product graph to construct rational yangian invariant solutions of the yang baxter equation in fundamental representations of cn and thence the full set of cn invariant factorized s matrices

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

yang baxter equation in long range interacting systems we consider the su p spin chains with long range interactions and the spin generalization of the calogero sutherland models we show that their properties derive from a transfer matrix obeying the yang baxter equation we obtain the expression of the conserved quantities of the dynamical models and we diagonalise them in the spin chain case we establish the connection between the degeneracies of the spectrum and the representation theory of the yangians we use a correspondence with the dynamical models to diagonalise the hamiltonian finally we extend the previous results to the case of a trigonometric r matrix

least squares solutions to ax b for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation abstract a matrix a r n n is called a bisymmetric matrix if its elements a i j satisfy the properties a i j a j i and a i j a n j 1 n i 1 for 1 i j n this paper considers least squares solutions to the matrix equation ax b for a under a central principal submatrix constraint and the optimal approximation a central principal submatrix is a submatrix obtained by deleting the same number of rows and columns in edges of a given matrix we first discuss the specified structure of bisymmetric matrices and their central principal submatrices then we give some necessary and sufficient conditions for the solvability of the least squares problem and derive the general representation of the solutions moreover we also obtain the expression of the solution to the corresponding optimal approximation problem

parabolic presentations of the super yangian y mathfrak gl _ m n associated with arbitrary 01 sequences let be an arbitrary composition of m n and let mathfrak s be an arbitrary 0 m 1 n sequence a new presentation depending on mu rm and mathfrak s of the super yangian ym n associated to the general linear lie superalgebra mathfrak gl m n is obtained

on the construction of a jacobi matrix from its mixed type eigenpairs in this paper an inverse eigenvalue problem of constructing a jacobi matrix from its mixedtype eigenpairs is considered the necessary and sufficient conditions for the existence and uniqueness of the solutions are derived one numerical algorithm and two numerical examples are given

quantum current algebras associated with rational r matrix abstract we study quantum current algebra a r associated with the rational r matrix of gl n and we give explicit formulae for the elements of its center at the critical level due to etingof kazhdan s construction the level c vacuum module v c r for the algebra a r possesses a quantum vertex algebra structure for any complex number c we prove that any module for the quantum vertex algebra v c r is naturally equipped with a structure of restricted a r module of level c and vice versa

yangian doubles of classical types and their vertex representations the yangian double dy gn is introduced for the classical types of gn o2n 1 sp2n and o2n via the gauss decomposition of the generator matrix the yangian double is given the drinfeld presentation in addition bosonization of level 1 realizations for the yangian double dy gn of non simply laced types are explicitly constructed

principal realization of the yangian y gl n motivated to simplify the structure of tensor representations we give a new set of generators for the yangian y sl n using the principal realization in simple lie algebras the isomorphism between our new basis and the standard cartan weyl basis is also given we show by example that the principal basis simplifies the yangian action significantly in the tensor product of the fundamental representation and its dual

implementation of curvilinear geometry into p version ht plate elements the formulation of the recently presented hybrid trefftz ht p version elements1 has thus far been restricted to straight sided polygonal elements the present paper removes this limitation two alternative formulations are studied in the first one any curvilinear geometry is represented accurately but the rigid body modes are recovered only in the limit as the p refinement level is increased in contrast the second formulation represents the rigid modes exactly while the actual curvilinear geometry is approached with increasing accuracy as the p refinement level is increased the practical efficiency of the two alternative approaches is studied and assessed on pertinent examples of thin plates in bending

rtt presentation of finite algebras we construct a wide class of finite algebras as truncations of yangians these truncations correspond to algebra homomorphisms and allow us to construct the algebras as exchange algebras the r matrix being the yangian one as an application we classify all irreducible finite dimensional representations of these algebras and determine their centre

rational and polynomial representations of yangians abstract we define natural classes of rational and polynomial representations of the yangian of the general linear lie algebra we also present the classification and explicit realizations of all irreducible rational representations of the yangian

center of the quantum affine vertex algebra in type a abstract we consider the quantum vertex algebra associated with the double yangian in type a as defined by etingof and kazhdan we show that its center is a commutative associative algebra and construct algebraically independent families of topological generators of the center at the critical level

structure of the string r matrix by requiring invariance directly under the yangian symmetry we rederive beisert s quantum r matrix in a form that carries explicit dependence on the representation labels the braiding factors and the spectral parameters ui in this way we demonstrate that there exists rewriting of its entries such that the dependence on the spectral parameters is purely of a difference form namely the latter enter only in the combination u1 u2 as indicated by the shift automorphism of the yangian when recasted in this fashion the entries exhibit a cleaner structure which allows us to spot new interesting relations among them this permits us to package them into a practical tensorial expression where the nondiagonal entries are taken care of by explicit combinations of symmetry algebra generators

a family of quadrilateral hybrid trefftz p elements for thick plate analysis abstract this paper presents a family of quadrilateral hybrid trefftz ht p elements based on reissner mindlin theory of moderately thick plates as compared with existing higher order ht thick plate elements j petrolito which make use of an incomplete set of polynomial homogeneous solutions for the internal displacement and rotation fields and of an auxiliary conforming frame field involving independently interpolated boundary distributions of displacements and rotations the new elements differ essentially with respect to the following two points 1 a t complete set of homogeneous solutions including polynomial and nonpolynomial functions has been derived and used to represent the intraelement displacement and rotations fields 2 the displacement component of the auxiliary frame field has been linked with the tangential component of the rotation so as to satisfy a particular constraint derived from equilibrium considerations the practical efficiency of these modifications has been assessed through a series of numerical examples which have shown that the new p elements are robust more accurate in terms of the number of unknowns and of the computational effort and that they do not lock in the thin limit

on a class of representations of the yangian and moduli space of monopoles a new class of infinite dimensional representations of the yangians yopen image in new window and yopen image in new window corresponding to a complex semisimple algebra open image in new window and its borel subalgebra open image in new window is constructed it is based on the generalization of the drinfeld realization of open image in new window in terms of quantum minors to the case of an arbitrary semisimple lie algebra open image in new window the poisson geometry associated with the constructed representations is described in particular it is shown that the underlying symplectic leaves are isomorphic to the moduli spaces of g monopoles defined as the components of the space of based maps of 1 into the generalized flag manifold open image in new window thus the constructed representations of the yangian may be considered as a quantization of the moduli space of the monopoles

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

rational r matrices centralizer algebras and tensor identities for e6 and e7 exceptional families of lie algebras we use cvitanovic s group theory princeton university press princeton nj in press http www nbi dk grouptheory phys rev d 14 1536 1976 diagrammatic techniques to construct the rational solutions of the yang baxter equation yang baxter equation in integrable systems edited by m jimbo advanced series in mathematical physics vol 10 world scientific singapore 1990 associated with the e6 and e7 families of lie algebras and thus explain westbury s j phys a 36 2857 2003 observations about their uniform spectral decompositions in doing so we explore the extensions of the brauer and symmetric group algebras to the centralizer algebras of e7 and e6 on their lowest dimensional representations and up to threefold tensor products thereof giving bases for them and a range of identities satisfied by the algebras defining invariant tensors

hopf structure of the yangian y sln in the drinfel d realization the yangian of the lie algebra sln is known to have different presentations in particular the rtt realization and the drinfel d realization using the isomorphism between them the explicit expressions of the comultiplication the antipode and the counit in the drinfel d realization of the yangian y sln are given as examples the cases of y sl2 and y sl3 are worked out

quantum superalgebras at roots of unity and non abelian symmetries of integrable models we consider integrable vertex models whose boltzmann weights r matrices are trigonometric solutions to the graded yang baxter equation as is well known the latter can be generically constructed from quantum affine superalgebras uq these algebras do not form a symmetry algebra of the model for generic values of the deformation parameter q when periodic boundary conditions are imposed if q is evaluated at a root of unity we demonstrate that in certain commensurate sectors one can construct non abelian subalgebras which are translation invariant and commute with the transfer matrix and therefore with all charges of the model in the line of argument we introduce the restricted quantum superalgebra uresq and investigate its root of unity limit we prove several new formulae involving supercommutators of arbitrary powers of the chevalley serre generators and derive higher order quantum serre relations as well as an analogue of lustzig s quantum frobenius theorem for superalgebras

r matrix realization of two parameter quantum affine algebra ur s glˆn we introduce the two parameter quantum affine algebra ur s gl n via the rtt realization the drinfeld realization is given and the type a quantum affine algebra is proved to be a special subalgebra of our extended algebra