1999/05/31 by Denis Uglov, Uglov, Denis
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #math.QA
paper · pdf · doi:10.48550/arxiv.math/9905196
LaTeX2e, 53 pages
arxiv created 1999/05/31 · arxiv updated 2009/11/30
The aim of this paper is to generalize several aspects of the recent work of Leclerc-Thibon and Varagnolo-Vasserot on the canonical bases of the level 1 q-deformed Fock spaces due to Hayashi. Namely, we define canonical bases for the higher-level q-deformed Fock spaces of Jimbo-Misra-Miwa-Okado and establish a relation between these bases and (parabolic) Kazhdan-Lusztig polynomials for the affine Weyl group of type A(1)r-1. As an application we derive an inversion formula for a sub-family of these polynomials. This article is an extended version of math.QA/9901032