We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebra Uq(ŝl2) in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of Z. Schur functions are realized as certain orthonormal basis vectors in the vertex representation associated to the standard Heisenberg algebra. In this picture the Littlewood-Ric...

We give new proofs of the rationality of the N = 1 superconformal minimal model vertex operator superalgebras and of the classification of their modules in both the Neveu-Schwarz and Ramond sectors. For this, we combine the standard free field realisation with the theory of Jack symmetric functions. A key role is played by Jack symmetric polynomials with a certain negative parameter that are la...

In this paper we establish some symmetric identities on a sequence of polynomials in an elementary way, and some known identities involving Bernoulli and Euler numbers and polynomials are obtained as particular cases.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In [4], we studied the (h, q)-tangent numbers and polynomials. By using these numbers and polynomials, we give some interesting symmetric properties for the (h, q)-tangent polynomials.

In this paper, we introduce the notion of Dunkl-classical orthogonal polynomials. Then, we show that generalized Hermite and generalized Gegenbauer polynomials are the only Dunkl-classical symmetric orthogonal polynomials by solving a suitable differential-difference equation. 2006 Elsevier Inc. All rights reserved.

In Stanley [8] the author introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. In [9] the same author gives a conjectured combinatorial interpretation for the coefficients of the polynomials. Here, we prove the conjecture for the terms of highest degree.

In Stanley [8], the author introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. In [9], the same author gives a conjectured combinatorial interpretation for the coefficients of the polynomials. Here, we prove the conjecture for the terms of highest degree.

A nonrecursive scheme is presented to compute the KazhdanLusztig polynomials associated to a classical Hermitian symmetric space, extending a result of Lascoux-Schutzenberger for grassmannians. The polynomials for the exceptional Hermitian domains are also tabulated. All the KazhdanLusztig polynomials considered are shown to be monic.

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group. 2000 Mathematics Subject Classification: 05...