Rogawski's conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A

Details Rogawski's conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A Rogawski's conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A

1998-05-07

arxiv.org/abs/math/9805035v1

Mathematics

Quantum Algebra

AMS-LaTex, 20 pages,no figures

Scientific paper

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_l. 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 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 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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