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.
ASJC Scopus subject areas
- Mathematics (miscellaneous)