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Locally analytic
representations and sheaves on the Bruhat–Tits building
Deepam Patel, Tobias Schmidt and Matthias Strauch |
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Vol. 8 (2014), No. 6, 1365–1445
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Abstract |
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Let be a finite field extension of and let be the group of -rational points of a split connected reductive group over . We view as a locally -analytic group with Lie algebra . The purpose of this work is to propose a construction which extends the localization of smooth -representations of P. Schneider and U. Stuhler to the case of locally analytic -representations. We define a functor from admissible locally analytic -representations with prescribed infinitesimal character to a category of equivariant sheaves on the Bruhat–Tits building of . For smooth representations, the corresponding sheaves are closely related to the sheaves of Schneider and Stuhler. The functor is also compatible, in a certain sense, with the localization of -modules on the flag variety by A. Beilinson and J. Bernstein. |
Keywords
locally analytic representations, Bruhat–Tits, buildings,
sheaves
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Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 20G25, 20G05, 32C38, 11S37, 13N10
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Milestones
Received: 27 November 2012
Revised: 20 February 2014
Accepted: 23 May 2014
Published: 2 October 2014
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Authors |
| Deepam Patel | |
| Department of Mathematics Purdue University 150 North University Street West Lafayette, IN 47907 United States |
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| Tobias Schmidt | |
| Institut fuer Mathematik Humboldt-Universität zu Berlin Rudower Chaussee 25 D-12489 Berlin Germany |
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| Matthias Strauch | |
| Department of Mathematics Indiana University Rawles Hall Bloomington, IN 47405 United States |
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