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2009 Motivic Proof of a Character Formula for SL(2)
Clifton Cunningham, Julia Gordon
Experiment. Math. 18(1): 11-44 (2009).

Abstract

This paper provides a proof of a $p$-adic character formula by means of motivic integration. We use motivic integration to produce virtual Chow motives that control the values of the characters of all depth-zero supercuspidal representations on all topologically unipotent elements of $p$}-adic $\SL(2)$; likewise, we find motives for the values of the Fourier transform of all regular elliptic orbital integrals having minimal nonnegative depth in their own Cartan subalgebra, on all topologically nilpotent elements of $p$-adic $\mathfrak{sl}(2)$. We then find identities in the ring of virtual Chow motives over $\mathbb{Q}$ that relate these two classes of motives. These identities provide explicit expressions for the values of characters of all depth-zero supercuspidal representations of $p$}-adic $\SL(2)$ as linear combinations of Fourier transforms of semisimple orbital integrals, thus providing a proof of a $p$-adic character formula.

Citation

Download Citation

Clifton Cunningham. Julia Gordon. "Motivic Proof of a Character Formula for SL(2)." Experiment. Math. 18 (1) 11 - 44, 2009.

Information

Published: 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1179.22018
MathSciNet: MR2548984

Subjects:
Primary: 22E50
Secondary: 03C10

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 1 • 2009
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