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Character values and Hochschild homology. (arXiv:1803.09442v2 [math.RT] UPDATED)
来源于:arXiv
We present a conjecture (and a proof for G=SL(2)) generalizing a result of J.
Arthur which expresses a character value of a cuspidal representation of a
$p$-adic group as a weighted orbital integral of its matrix coefficient. It
also generalizes a conjecture by the second author proved by Schneider-Stuhler
and (independently) the first author. The latter statement expresses an
elliptic character value as an orbital integral of a pseudo-matrix coefficient
defined via the Chern character map taking value in zeroth Hochschild homology
of the Hecke algebra. The present conjecture generalizes the construction of
pseudo-matrix coefficient using compactly supported Hochschild homology, as
well as a modification of the category of smooth representations, the so called
compactified category of smooth $G$-modules. This newly defined "compactified
pseudo-matrix coefficient" lies in a certain space on which the weighted
orbital integral is a conjugation invariant linear functional, our conjecture 查看全文>>