Rogawski’s conjecture on the Jantzen filtration for the degenerate affine hecke algebra of type a

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Abstract

The functors constructed by Arakawa and the author relate the representation theory of glnand that of the degenerate affine Hecke algebra Hof GL. They transform the Verma modules over glnto the standard modules over H`. 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 Hby translating the corresponding results for glnthrough the functors: (i) the (generalized) Bernstein-Gelfand-Gelfand resolution for a certain class of simplemodules, (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.

Original languageEnglish
Pages (from-to)393-409
Number of pages17
JournalRepresentation Theory
Volume2
Issue number11
DOIs
Publication statusPublished - Oct 26 1998
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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