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15 March 2007 Invariant distributions on p-adic analytic groups
Jan Kohlhaase
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Duke Math. J. 137(1): 19-62 (15 March 2007). DOI: 10.1215/S0012-7094-07-13712-8

Abstract

Let p be a prime number, let L be a finite extension of the field Qp of p-adic numbers, let K be a spherically complete extension field of L, and let G be the group of L-rational points of a split reductive group over L. We derive several explicit descriptions of the center of the algebra D(G,K) of locally analytic distributions on G with values in K. The main result is a generalization of an isomorphism of Harish-Chandra which connects the center of D(G,K) with the algebra of Weyl-invariant, centrally supported distributions on a maximal torus of G. This isomorphism is supposed to play a role in the theory of locally analytic representations of G as studied by P. Schneider and J. Teitelbaum

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Jan Kohlhaase. "Invariant distributions on p-adic analytic groups." Duke Math. J. 137 (1) 19 - 62, 15 March 2007. https://doi.org/10.1215/S0012-7094-07-13712-8

Information

Published: 15 March 2007
First available in Project Euclid: 8 March 2007

zbMATH: 1133.11066
MathSciNet: MR2309143
Digital Object Identifier: 10.1215/S0012-7094-07-13712-8

Subjects:
Primary: 11S80, 16S30, 16U70, 22E50

Rights: Copyright © 2007 Duke University Press

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Vol.137 • No. 1 • 15 March 2007
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