Locally analytic representations and sheaves on the Bruhat-Tits building

Abstract

Let L be a finite field extension of Q_p and let G be the group of L-rational points of a split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. We define a functor from admissible locally analytic G-representations with prescribed infinitesimal character to a category of equivariant sheaves on the Bruhat-Tits building of G. For smooth representations, the corresponding sheaves are closely related to the sheaves constructed by S. Schneider and U. Stuhler. The functor is also compatible, in a certain sense, with the localization of g-modules on the flag variety by A. Beilinson and J. Bernstein.

Replaces earlier version. Exposition shortened and improved in several places, and new material and examples added. In particular, section 11 is new."

References in corpus (3)

• Algebras of p-adic distributions and admissible representations
• On the irreducibility of locally analytic principal series representations
• Some complements to the Lazard isomorphism