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

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

2010-04-28

arxiv.org/abs/1004.5032v1

Mathematics

Representation Theory

59 pages

Scientific paper

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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