Dimensions of quantized tilting modules

1999/02/15 by Viktor Ostrik, Ostrik, Viktor
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9902093

6 pages, LaTex2e, submitted to Moscow Math. Journal

openalex publication_date 1999/02/15 · arxiv created 2000/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U be the quantum group with divided powers in p-th root of unity for prime p. For any two-sided cell A in the corresponding affine Weyl group one associates tensor ideal in the category of tilting modules over U. In this note we show that for any cell A there exists tilting module T from the corresponding tensor ideal such that biggest power of p which divides dim T is p^a(A) where a(A) is Lusztig's a-function. In new version some typos are corrected and exposition is improved following suggestions of the referee.

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