An exotic Deligne-Langlands correspondence for symplectic groups
By Syu Kato. 2006
107 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/071536e2399832dfa3ada0aa182d97d53bdc241b
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Citations in the corpus
- On the classification of irreducible representations of affine Hecke algebras with unequal parameters (2010, background): “ralization, much less is known about affine Hecke algebras with unequal parameters. The reason is that Lusztig’s constructions in equivariant K-theory [KaLu1] allow only one deformation parameter. Kato [Kat2] invented a more complicated variety, called an exotic nilpotent cone, which plays a similar r”
- Orbit closures in the enhanced nilpotent cone (2007, background): “6. Connections withKato’s ExoticNilpotentCone In this section, we discuss the analogy between the enhanced nilpotent cone V× N studied in this paper and the exotic nilpotent cone N studied by Kato in [K1], [K2], [K3]. (We assume that charF6= 2.) To make a concrete connection, we choose the symplecti”