Dimensions of quantized tilting modules

Details Dimensions of quantized tilting modules Dimensions of quantized tilting modules

1999-02-15

arxiv.org/abs/math/9902093v2

Mathematics

Quantum Algebra

6 pages, LaTex2e, submitted to Moscow Math. Journal

Scientific paper

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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