Some consequences of Harish-Chandra's submersion principle

Authors:
Cary Rader and Allan Silberger

Journal:
Proc. Amer. Math. Soc. **118** (1993), 1271-1279

MSC:
Primary 22E50

MathSciNet review:
1169888

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Abstract: Let be a reductive -adic group, a good maximal compact subgroup, any open subgroup, and an admissible representation of of finite type. In *A submersion principle and its applications*, Harish-Chandra proves the theorem that is a finite-rank operator for in the regular set in order to show that the character is a locally constant class function on . From this, the authors derive the formula for any -finite matrix coefficient of a discrete series representation with formal degree . They use another technical result of the paper to prove that invariant integrals of Schwartz space functions converge absolutely. None of these results depends upon a characteristic zero assumption.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1169888-X

Keywords:
Character,
discrete series,
reductive -adic groups,
Schwartz space,
invariant integral

Article copyright:
© Copyright 1993
American Mathematical Society