Motivic proof of a character formula for SL(2)

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dc.creatorCunningham, Clifton
dc.creatorGordon, Julia
dc.date2006-09-09
dc.date2008-08-19
dc.date.accessioned2026-07-07T09:57:11Z
dc.date.available2026-07-07T09:57:11Z
dc.descriptionWe give a motivic proof of a character formula for depth zero supercuspidal representations of $p$-adic SL(2). We begin by finding the virtual Chow motives for the character values of all depth zero supercuspidal representations of $p$-adic SL(2), at topologically unipotent elements. Then we find the virtual Chow motives for the values of the Fourier transform of all regular elliptic orbital integrals with depth zero in their Cartan subalgebra, at topologically nilpotent elements. Finally, we prove a character formula for depth zero supercuspidal representations by showing that the formula corresponds to three identities in the ring of virtual Chow motives over $\mathbb{Q}$.
dc.description51 pages; to appear in Experimental Mathematics
dc.identifierhttps://arxiv.org/abs/math/0609260
dc.identifierhttp://arxiv.org/abs/math/0609260
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167252
dc.subjectRepresentation Theory
dc.subjectLogic
dc.subject22E50; 03C10
dc.titleMotivic proof of a character formula for SL(2)
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