Smooth representations of GL(m,D), V: Endo-classes

2010/04/28 by Paul Broussous, Vincent Sécherre, Broussous, Paul +3
Mathematics · #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.1004.5032

59 pages

arxiv created 2010/04/28 · arxiv updated 2010/04/29

Abstract

Let F be a locally compact nonarchimedean local field. In this article, we extend to any inner form of GL(n) over F the notion of endo-class introduced by Bushnell and Henniart for GL(n,F). We investigate the intertwining relations of simple characters of these groups, in particular their preservation properties under transfer. This allows us to associate to any discrete series representation of an inner form of GL(n,F) an endo-class over F. We conjecture that this endo-class is invariant under the local Jacquet-Langlands correspondence.

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