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Steinberg representations and harmonic cochains for split adjoint quasi-simple groups (1708.00717v1)
Published 2 Aug 2017 in math.RT
Abstract: Let $G$ be an adjoint quasi-simple group defined and split over a non-archimedean local field $K$. We prove that the dual of the Steinberg representation of $G$ is isomorphic to a certain space of harmonic cochains on the Bruhat-Tits building of $G$. The Steinberg representation is considered with coefficients in any commutative ring.
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