### Abstract

The functors constructed by Arakawa and the author relate the representation theory of gl_{n}and that of the degenerate affine Hecke algebra H_{ℓ}of GL_{ℓ}. They transform the Verma modules over gl_{n}to 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 H_{ℓ}by translating the corresponding results for gl_{n}through 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 language | English |
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Pages (from-to) | 393-409 |

Number of pages | 17 |

Journal | Representation Theory |

Volume | 2 |

Issue number | 11 |

DOIs | |

Publication status | Published - Oct 26 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**Rogawski’s conjecture on the Jantzen filtration for the degenerate affine hecke algebra of type a.** / Suzuki, Takeshi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Rogawski’s conjecture on the Jantzen filtration for the degenerate affine hecke algebra of type a

AU - Suzuki, Takeshi

PY - 1998/10/26

Y1 - 1998/10/26

N2 - The functors constructed by Arakawa and the author relate the representation theory of glnand that of the degenerate affine Hecke algebra Hℓof GLℓ. 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 Hℓby 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.

AB - The functors constructed by Arakawa and the author relate the representation theory of glnand that of the degenerate affine Hecke algebra Hℓof GLℓ. 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 Hℓby 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.

UR - http://www.scopus.com/inward/record.url?scp=85009789234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009789234&partnerID=8YFLogxK

U2 - 10.1090/S1088-4165-98-00043-0

DO - 10.1090/S1088-4165-98-00043-0

M3 - Article

AN - SCOPUS:85009789234

VL - 2

SP - 393

EP - 409

JO - Representation Theory

JF - Representation Theory

SN - 1088-4165

IS - 11

ER -