Rogawski's conjecture on the Jantzen

filtration for the degenerate affine

Hecke algebra of type

Author:
Takeshi Suzuki

Journal:
Represent. Theory **2** (1998), 393-409

MSC (1991):
Primary 22E50; Secondary 17B10

DOI:
https://doi.org/10.1090/S1088-4165-98-00043-0

Published electronically:
October 26, 1998

MathSciNet review:
1651408

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The functors constructed by Arakawa and the author relate the representation theory of and that of the degenerate affine Hecke algebra of . They transform the Verma modules over to the standard modules over . 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 by translating the corresponding results for 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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Additional Information

**Takeshi Suzuki**

Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Japan

Email:
takeshi@kurims.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S1088-4165-98-00043-0

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.

Article copyright:
© Copyright 1998
American Mathematical Society