An exotic Deligne-Langlands correspondence for symplectic groups

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.

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

References in corpus (2)

• Orbit closures in the enhanced nilpotent cone
• Mirabolic affine Grassmannian and character sheaves

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• The exotic Robinson-Schensted correspondence
• Duality for Ext-groups and extensions of discrete series for graded Hecke algebras
• Affine Hecke algebras and their representations
• A uniform classification of discrete series representations of affine Hecke algebras
• Equivariant coherent sheaves on the exotic nilpotent cone
• Irreducible components of exotic Springer fibres
• The mirabolic Hecke algebra
• Normality of orbit closures in the enhanced nilpotent cone
• Point stabilisers for the enhanced and exotic nilpotent cones
• Irreducible Components of Exotic Springer fibres II: The Exotic Robinson-Schensted Algorithm
• Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
• Enhanced adjoint action and their orbits for the general linear group
• Exotic Springer fibers for orbits corresponding to one-row bipartitions