Rogawski's conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A
Abstract
The functors constructed by Arakawa and the author relate the representation theory of gln and that of the degenerate affine Hecke algebra Hl of GLl. They transform the Verma modules over gln to the standard modules over Hl. They transform the simple modules to the simple modules. 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 Hl by translating the corresponding results for gln 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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