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

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


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.


Singular Vector Canonical Basis Irreducible Module Wedge Product Crystal Graph 
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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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