RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mosc. Math. J.: Year: Volume: Issue: Page: Find

 Mosc. Math. J., 2001, Volume 1, Number 1, Pages 65–71 (Mi mmj12)

Dimensions of quantized tilting modules

V. V. Ostrik

Massachusetts Institute of Technology

Abstract: Let $U$ be the quantum group with divided powers at $p$-th root of unity for prime $p$. To any two-sided cell $A$ in the corresponding affine Weyl group, one associates the tensor ideal in the category of tilting modules over $U$. In this note we show that for any cell $A$ there exists a tilting module $T$ from the corresponding tensor ideal such that the greatest power of $p$ which divides $\dim T$ is $p^{a(A)}$, where $a(A)$ is Lusztig's $a$-function. This result is motivated by a conjecture of J. Humphreys.

Key words and phrases: Quantum groups at roots of unity, tilting modules, special representations of Weyl groups.

DOI: https://doi.org/10.17323/1609-4514-2001-1-1-65-71

Full text: http://www.ams.org/.../abstracts-1-1.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 20G05; Secondary 17B37
Received: September 12, 2000; in revised form December 4, 2000

Citation: V. V. Ostrik, “Dimensions of quantized tilting modules”, Mosc. Math. J., 1:1 (2001), 65–71

Citation in format AMSBIB
\Bibitem{Ost01} \by V.~V.~Ostrik \paper Dimensions of quantized tilting modules \jour Mosc. Math.~J. \yr 2001 \vol 1 \issue 1 \pages 65--71 \mathnet{http://mi.mathnet.ru/mmj12} \crossref{https://doi.org/10.17323/1609-4514-2001-1-1-65-71} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1852934} \zmath{https://zbmath.org/?q=an:0986.20046}