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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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}


Linking options:
  • http://mi.mathnet.ru/eng/mmj12
  • http://mi.mathnet.ru/eng/mmj/v1/i1/p65

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Moscow Mathematical Journal
    Number of views:
    This page:141
    References:25

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020