Duke Mathematical Journal
- Duke Math. J.
- Volume 137, Number 1 (2007), 19-62.
Invariant distributions on -adic analytic groups
Let be a prime number, let be a finite extension of the field of -adic numbers, let be a spherically complete extension field of , and let be the group of -rational points of a split reductive group over . We derive several explicit descriptions of the center of the algebra of locally analytic distributions on with values in . The main result is a generalization of an isomorphism of Harish-Chandra which connects the center of 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 as studied by P. Schneider and J. Teitelbaum
Duke Math. J., Volume 137, Number 1 (2007), 19-62.
First available in Project Euclid: 8 March 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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