Geodesic
Smooth representations of ${GL}_m(D)$. V: Endo-classes
Documenta mathematica, Tome 17 (2012), pp. 23-77.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $\F$ be a locally compact nonarchimedean local field. In this article, we extend to any inner form of $\GL_n$ over $\F$, with $n\>1$, 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.
Classification : 22E50
Keywords: representations of $p$-adic groups, sim­ple characters, type theory, shintani lift, Jacquet-lang­lands correspondence 
@article{DOCMA_2012__17__a28,
     author = {Broussous, P. and S\'echerre, V. and Stevens, S.},
     title = {Smooth representations of ${GL}_m(D)$. {V:} {Endo-classes}},
     journal = {Documenta mathematica},
     pages = {23--77},
     publisher = {mathdoc},
     volume = {17},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a28/}
}
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Broussous, P.; Sécherre, V.; Stevens, S. Smooth representations of ${GL}_m(D)$. V: Endo-classes. Documenta mathematica, Tome 17 (2012), pp. 23-77. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a28/