Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On decomposition numbers with Jantzen filtration of cyclotomic $q$-Schur algebras
HTML articles powered by AMS MathViewer

by Kentaro Wada
Represent. Theory 14 (2010), 417-434
Published electronically: May 18, 2010


Let $\mathscr {S}(\varLambda )$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $\mathscr {H}_{n,r}$, introduced by Dipper, James and Mathas. In this paper, we consider $v$-decomposition numbers of $\mathscr {S}(\varLambda )$, namely decomposition numbers with respect to the Jantzen filtrations of Weyl modules. We prove, as a $v$-analogue of the result obtained by Shoji and Wada, a product formula for $v$-decomposition numbers of $\mathscr {S}(\varLambda )$, which asserts that certain $v$-decomposition numbers are expressed as a product of $v$-decomposition numbers for various cyclotomic $q$-Schur algebras associated to Ariki-koike algebras $\mathscr {H}_{n_i,r_i}$ of smaller rank. Moreover, we prove a similar formula for $v$-decomposition numbers of $\mathscr {H}_{n,r}$ by using a Schur functor.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20-XX, 16-XX
  • Retrieve articles in all journals with MSC (2010): 20-XX, 16-XX
Bibliographic Information
  • Kentaro Wada
  • Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
  • Address at time of publication: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
  • Email:
  • Received by editor(s): November 6, 2007
  • Published electronically: May 18, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 14 (2010), 417-434
  • MSC (2010): Primary 20-XX, 16-XX
  • DOI:
  • MathSciNet review: 2652073