Duke Mathematical Journal

An exotic Deligne-Langlands correspondence for symplectic groups

Syu Kato

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Abstract

Let G=Sp(2n,C) be a complex symplectic group. We introduce a (G×(C×)+1)-variety N, which we call the -exotic nilpotent cone. Then, we realize the Hecke algebra H of type Cn(1) with three parameters via equivariant algebraic K-theory in terms of the geometry of N2. This enables us to establish a Deligne-Langlands–type classification of simple H-modules under a mild assumption on parameters. As applications, we present a character formula and multiplicity formulas of H-modules

Article information

Source
Duke Math. J. Volume 148, Number 2 (2009), 305-371.

Dates
First available in Project Euclid: 22 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1242998669

Digital Object Identifier
doi:10.1215/00127094-2009-028

Mathematical Reviews number (MathSciNet)
MR2524498

Zentralblatt MATH identifier
1183.20002

Subjects
Primary: 20G99: None of the above, but in this section

Citation

Kato, Syu. An exotic Deligne-Langlands correspondence for symplectic groups. Duke Math. J. 148 (2009), no. 2, 305--371. doi:10.1215/00127094-2009-028. https://projecteuclid.org/euclid.dmj/1242998669


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