### 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)