On the Steinberg character of a semisimple p-adic group

Details On the Steinberg character of a semisimple p-adic group On the Steinberg character of a semisimple p-adic group

2012-04-20

arxiv.org/abs/1204.4712v1

Mathematics

Representation Theory

4 pages

Scientific paper

Let G be a simply connected almost simple algebraic group defined and split over a nonarchimedean local field K and let S be the Steinberg representation of G(K). Let t be a very regular split semisimple element of G(K). In this paper we give a simple formula (not as an alternating sum) for the value of the character of S at t; we show that this value is an integer power of q, the cardinal of the residue field of K.

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