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A factorization result for classical and similitude groups

  • Alan Roche,
    Dept. of Mathematics, University of Oklahoma, Norman, OK, USA
  • C. Ryan Vinroot,
    Dept. of Mathematics, College of William and Mary, Williamsburg, VA, USA
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Abstract

For most classical and similitude groups, we show that each element can be written as a product of two transformations that a) preserve or almost preserve the underlying form and b) 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: classical group, similitude group, involution, $p$-adic group, dual of representation classical group, similitude group, involution, $p$-adic group, dual of representation
MSC Classifications: 20G15, 22E50 show english descriptions Linear algebraic groups over arbitrary fields
Representations of Lie and linear algebraic groups over local fields [See also 20G05]
20G15 - Linear algebraic groups over arbitrary fields
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
 

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