Symmetric Polynomials and U_q(sl₂)

1999/02/28 by Naihuan Jing
Mathematics · #math.QA #math.CO

paper · pdf

published as Represent. Theory 4 (2000), 46-63. · Revised version, 17 pages, AMSLaTex

arxiv created 1999/06/23 · arxiv updated 2009/11/30

Abstract

We study the explicit formula of Lusztig's integral forms of the level one quantum affine algebra U_q(sl₂) in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of \mathbb 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 \mathbb Z[q, q]-form of U_q(sl₂) on Schur polynomials.

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