Algebra & Number Theory
- Algebra Number Theory
- Volume 8, Number 6 (2014), 1365-1445.
Locally analytic representations and sheaves on the Bruhat–Tits building
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.
Algebra Number Theory, Volume 8, Number 6 (2014), 1365-1445.
Received: 27 November 2012
Revised: 20 February 2014
Accepted: 23 May 2014
First available in Project Euclid: 20 December 2017
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Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 20G25: Linear algebraic groups over local fields and their integers 20G05: Representation theory 32C38: Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15] 11S37: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Patel, Deepam; Schmidt, Tobias; Strauch, Matthias. Locally analytic representations and sheaves on the Bruhat–Tits building. Algebra Number Theory 8 (2014), no. 6, 1365--1445. doi:10.2140/ant.2014.8.1365. https://projecteuclid.org/euclid.ant/1513730251