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Canonical Bases of Higher-Level q-Deformed Fock Spaces and Kazhdan-Lusztig Polynomials

  • Denis Uglov
Chapter
Part of the Progress in Mathematics book series (PM, volume 191)

Abstract

The aim of this paper is to generalize some aspects of the recent work of Leclerc-Thibon and Varagnolo-Vasserot on the canonical bases of the level 1 q-deformed Fock spaces of 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 r-1 (1) . As an application, we derive an inversion formula for a subfamily of these polynomials.

Keywords

Singular Vector Canonical Basis Irreducible Module Wedge Product Crystal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Denis Uglov
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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