Quantum Algebra papers

We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations…

We consider the quantized Knizhnik-Zamolodchikov-Bernard difference equation (qKZB) with step p and values in a tensor product of finite dimensional evaluation modules over the elliptic quantum…

We consider functions on the lattice generated by the integer powers of q2 for 0<q<1 and construct the q-analog of Fourier transform based on the Jackson integral in the space of distributions…

We construct an integral representation of eigenfunctions for Macdonald's q-difference operator associated with the root system of type Cn . It is given in terms of a restriction of a…

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted…

In this elementary paper we prove that the extra vanishing property characterizes the BC interpolation Macdonald polynomials inside a very general class of multivariate interpolation polynomials. It…

In this note we give a short proof of Cherednik's generalization of Macdonald-Mehta identities for the root system An-1 using the representation theory of quantum groups. These identities,…

For each of the classical Lie algebras g(n)=o(2n+1), sp(2n), o(2n) of type B, C, D we consider the centralizer of the subalgebra g(n-m) in the universal enveloping algebra U(g(n)). We show that…

Givental's recursion relations for the flag varieties G/B are established.

We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do so. On the other…

We present a definition of an invariant #(M,H), defined for every finite-dimensional Hopf algebra (or Hopf superalgebra or Hopf object) H and for every closed, framed 3-manifold M. When H is a…

We compare two natural bases for the invariant space of a tensor product of irreducible representations of A2, or sl(3). One basis is the web basis, defined from a skein theory called the…

The goal of the present paper is to find higher genus surgery formulae for the set of finite-type invariants of homology spheres, and to develop a companion theory of finite-type invariants to be…

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of…

Deformed Harmonic Oscillator Algebras are generated by four operators, two mutually adjoint a and a, and two self-adjoint N and the unity 1 such as: $[a,N] = a, [a, N]=…

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations.…

We study a q-deformation for the semi-direct product of the symmetric group Sn with the Clifford algebra on n anticommuting generators. We obtain a q-version of the projective analogue for…

The construction of Lie bialgebra from double Lie algebra is presented. It is used to relate some types of cobracket on inhomogenous so(p,q) algebras with double Lie algebra structures on so(p+1,q)…

In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving…

A new method for deriving universal R matrices from braid group representation is discussed. In this case, universal R operators can be defined and expressed in terms of products of braid…

We construct a universal trigonometric solution of the Gervais-Neveu-Felder equation in the case of finite dimensional simple Lie algebras and finite dimensional contragredient simple Lie…

A direct proof is given of the fact that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation.

We construct a solution of Cherednik's quantum Knizhnik Zamolodchikov equation associated with the root system of type Cn. This solution is given in terms of a restriction of a…

Explicit solutions of the quantum Yang-Baxter equation are given corresponding to the non-unitary solutions of the classical Yang-Baxter equation for sl(5).

Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf algebra over an algebraically closed field k of characteristic 0, then H is of Frobenius type (i.e. if V is an irreducible…