Locally analytic representations and sheaves on the Bruhat-Tits building

Details Locally analytic representations and sheaves on the Bruhat-Tits building Locally analytic representations and sheaves on the Bruhat-Tits building

2012-01-17

arxiv.org/abs/1201.3646v2

Mathematics

Representation Theory

78 pages

Scientific paper

Let p be an odd prime and L a finite field extension of Q_p. Let G be the group of rational points of a L-split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. The purpose of this work is to propose a construction which extends the localization of smooth G-representations of P. Schneider and U. Stuhler to the case of locally analytic G-representations. In more concrete terms we construct a well-behaved functor from admissible locally analytic G-representations with prescribed infinitesimal character to a category of sheaves on the Bruhat-Tits building of G. The construction is also compatible, in a certain sense, with the localization of g-modules on the flag variety by A. Beilinson and J. Bernstein. This preprint is a replacement of a former version. Some minor items are corrected.

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