Motivic nature of character values of depth-zero representations

Julia Gordon

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arXiv · math/0403529

Motivic nature of character values of depth-zero representations

Julia Gordon

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Abstract

It is shown that the values of Harish-Chandra distribution characters on definable compact subsets of the set of topologically unipotent elements of symplectic or special orthogonal p-adic groups can be expressed as the trace of Frobenius action on virtual Chow motives. The result is restricted to a class of depth-zero representations that can be obtained by inflation from Deligne-Lusztig representations. The proof relies on arithmetic motivic integration.

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Julia Gordon. 2004-03-31. Motivic nature of character values of depth-zero representations. https://arxiv.org/abs/math/0403529

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