Vol. 307, No. 2, 2020

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Globally analytic principal series representation and Langlands base change

Jishnu Ray

Vol. 307 (2020), No. 2, 455–490
Abstract

S. Orlik and M. Strauch have studied locally analytic principal series representation for general p-adic reductive groups generalizing an earlier work of P. Schneider for GL(2) and related the condition of irreducibility of such locally analytic representation with that of a suitable Verma module. We take the case of GL(n) and study the globally analytic principal series representation under the action of the pro-p Iwahori subgroup of GL(n, p), following the notion of globally analytic representations introduced by M. Emerton. Furthermore, we relate the condition of irreducibility of our globally analytic principal series to that of a Verma module. Finally, using the Steinberg tensor product theorem, we construct the Langlands base change of our globally analytic principal series to a finite unramified extension of p.

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Keywords
rigid analytic representations, Tate algebra, affinoids, rigid analytic geometry, $p$-adic Langlands, $p$-adic representations, $p$-adic Lie groups
Mathematical Subject Classification 2010
Primary: 20G25, 22E50
Secondary: 20G05
Milestones
Received: 22 September 2018
Revised: 27 February 2020
Accepted: 5 March 2020
Published: 4 September 2020
Authors
Jishnu Ray
Department of Mathematics
The University of British Columbia
Vancouver BC
Canada