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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.

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Rogawski’s conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A
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by Takeshi Suzuki
Represent. Theory 2 (1998), 393-409
Published electronically: October 26, 1998


The functors constructed by Arakawa and the author relate the representation theory of $\mathfrak {gl}_n$ and that of the degenerate affine Hecke algebra $H_\ell$ of $\mathrm {GL}_\ell$. They transform the Verma modules over $\mathfrak {gl}_n$ to the standard modules over $H_\ell$. In this paper we prove that they transform the simple modules to the simple modules (in more general situations than in the previous paper). We also prove that they transform the Jantzen filtration on the Verma modules to that on the standard modules. We obtain the following results for the representations of $H_\ell$ by translating the corresponding results for $\mathfrak {gl}_n$ through the functors: (i) the (generalized) Bernstein-Gelfand-Gelfand resolution for a certain class of simple modules, (ii) the multiplicity formula for the composition series of the standard modules, and (iii) its refinement concerning the Jantzen filtration on the standard modules, which was conjectured by Rogawski.
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Bibliographic Information
  • Takeshi Suzuki
  • Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Japan
  • MR Author ID: 199324
  • Email:
  • Received by editor(s): January 23, 1998
  • Received by editor(s) in revised form: August 31, 1998
  • Published electronically: October 26, 1998
  • Additional Notes: The author is supported by the JSPS Research Fellowships for Young Scientists.
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 393-409
  • MSC (1991): Primary 22E50; Secondary 17B10
  • DOI:
  • MathSciNet review: 1651408