An exotic Deligne-Langlands correspondence for symplectic groups

Details An exotic Deligne-Langlands correspondence for symplectic groups An exotic Deligne-Langlands correspondence for symplectic groups

2006-01-08

arxiv.org/abs/math/0601155v7

Duke Math. J. 148 no.2 305--371 (2009)

Mathematics

Representation Theory

v7, 52pages. Corrected typos and errors in the proofs of Lemma 4.1 and Theorem 6.2 modulo Proposition 6.7, final version, acce

Scientific paper

10.1215/00127094-2009-028

Let G be a complex symplectic group. We introduce a G x (C ^x) ^{l + 1}-variety N_{l}, which we call the l-exotic nilpotent cone. Then, we realize the Hecke algebra H of type C_n ^(1) with three parameters via equivariant algebraic K-theory in terms of the geometry of N_2. This enables us to establish a Deligne-Langlands type classification of "non-critical" simple H-modules. As applications, we present a character formula and multiplicity formulas of H-modules.

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