Duke Mathematical Journal

Invariant distributions on p-adic analytic groups

Jan Kohlhaase

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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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Duke Math. J., Volume 137, Number 1 (2007), 19-62.

First available in Project Euclid: 8 March 2007

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Primary: 11S80: Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.) 16S30: Universal enveloping algebras of Lie algebras [See mainly 17B35] 16U70: Center, normalizer (invariant elements) 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]


Kohlhaase, Jan. Invariant distributions on $p$ -adic analytic groups. Duke Math. J. 137 (2007), no. 1, 19--62. doi:10.1215/S0012-7094-07-13712-8. https://projecteuclid.org/euclid.dmj/1173373450

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