Symmetric Polynomials and $U_q(\hat{sl}_2)$

Naihuan Jing

paper

Symmetric Polynomials and $U_{q} (s l^_{2})$

arXiv:math/9902109

Abstract

We study the explicit formula of Lusztig's integral forms of the level one quantum affine algebra $U_{q} (s l^_{2})$ 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-Richardson rule is expressed by integral formulas, and is used to define the action of Lusztig's $Z [q, q]$ -form of $U_{q} (s l^_{2})$ on Schur polynomials.

Revised version, 17 pages, AMSLaTex

Symmetric Polynomials and Uq​(sl^2​)

Abstract

Symmetric Polynomials and $U_{q} (s l^_{2})$