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 Locally analytic representations and sheaves on the Bruhat-Tits building


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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.



Autor: Deepam Patel; Tobias Schmidt; Matthias Strauch

Fuente: https://archive.org/







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