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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.


Kazhdan-Lusztig cells and decomposition numbers
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by Meinolf Geck
Represent. Theory 2 (1998), 264-277
Published electronically: June 15, 1998


We consider a generic Iwahori–Hecke algebra $H$ associated with a finite Weyl group. Any specialization of $H$ gives rise to a corresponding decomposition matrix, and we show that the problem of computing that matrix can be interpreted in terms of Lusztig’s map from $H$ to the asymptotic algebra $J$. This interpretation allows us to prove that the decomposition matrices always have a lower uni-triangular shape; moreover, we determine these matrices explicitly in the so-called defect $1$ case.
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Bibliographic Information
  • Meinolf Geck
  • Affiliation: UFR de Mathématiques and UMR 7586 du CNRS, Université Paris 7, 2 Place Jussieu, 75251 Paris, France
  • MR Author ID: 272405
  • Email:
  • Received by editor(s): December 11, 1997
  • Received by editor(s) in revised form: April 27, 1998
  • Published electronically: June 15, 1998
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 264-277
  • MSC (1991): Primary 20C20; Secondary 20G99
  • DOI:
  • MathSciNet review: 1628035