Canonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials

Details Canonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials Canonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials

1999-05-31

arxiv.org/abs/math/9905196v1

Mathematics

Quantum Algebra

LaTeX2e, 53 pages

Scientific paper

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

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