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WALDSPURGER'S INVOLUTION AND TYPES

Published online by Cambridge University Press:  03 December 2004

DAVID MANDERSCHEID
Affiliation:
Mathematics Department, University of Iowa, Iowa City, IA 52242, USAdavid-manderscheid@uiowa.edu
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Abstract

Waldspurger's involution for the genuine irreducible supercuspidal representations of $\widetilde{\mathrm{SL}_{2}(F)}$ is parametrized in terms of types in the case $F$$p$-adic with $p$ odd. In particular, it is shown that the in-volution is given by conjugating by an element of $\widetilde{\mathrm{GL}_{2}(F)}$ and twisting one of the defining parameters of an associated type by a quadratic character, the relevant parameter being a character on the norm one elements of a quadratic extension.

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

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Footnotes

Research supported in part by the NSA through grant MDA904-97-1-0046.