Steinberg representations and harmonic cochains for split adjoint quasi-simple groups

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.

preprint USTHB (2011)

References in corpus (1)

• Cohomology of Drinfeld symmetric spaces and Harmonic cochains