An exotic Deligne-Langlands correspondence for symplectic groups
Representation Theory
2019-12-19 v7 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.math/0601155,
title = {An exotic Deligne-Langlands correspondence for symplectic groups},
author = {Syu Kato},
journal= {arXiv preprint arXiv:math/0601155},
year = {2019}
}
Comments
v7, 52pages. Corrected typos and errors in the proofs of Lemma 4.1 and Theorem 6.2 modulo Proposition 6.7, final version, accepted for publication in Duke Math