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A Factorization Result for Classical and Similitude Groups

Published online by Cambridge University Press:  20 November 2018

Alan Roche  and
C. Ryan Vinroot
Alan Roche
Affiliation:
Dept. of Mathematics, University of Oklahoma, Norman, OK 73109-3103, USA, e-mail: aroche@math.ou.edu
C. Ryan Vinroot
Affiliation:
Dept. of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, USA e-mail: vinroot@math.wm.edu
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Abstract

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For most classical and similitude groups, we show that each element can be written as a product of two transformations that preserve or almost preserve the underlying form and whose squares are certain scalar maps. This generalizes work of Wonenburger and Vinroot. As an application, we re-prove and slightly extend a well-known result of Mœglin, Vignéras, and Waldspurger on the existence of automorphisms of $p$-adic classical groups that take each irreducible smooth representation to its dual.

Keywords

20G1522E50classical groupsimilitude groupinvolutionp-adic groupdual representation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 174 - 190
Copyright
Copyright © Canadian Mathematical Society 2018

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