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

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Let F be a locally compact nonarchimedean local field. In this article, we extend to any inner form of GLn​ over F, with n⩾1, the notion of endo-class introduced by Bush­nell and Henniart for GLn​(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 GLn​(F) an endo-class over F. We conjecture that this endo-class is invariant under the local Jacquet–Langlands correspondence.
DOI : 10.4171/dm/360
Classification : 22E50
Mots-clés : representations of p-adic groups, sim­ple characters, type theory, shintani lift, Jacquet-lang­lands correspondence 
P. Broussous; V. Sécherre; S. Stevens. Smooth representations of ${GL}_m(D)$. V: Endo-classes. Documenta mathematica, Tome 17 (2012), pp. 23-77. doi: 10.4171/dm/360
@article{10_4171_dm_360,
     author = {P. Broussous and V. S\'echerre and S. Stevens},
     title = {Smooth representations of ${GL}_m(D)$. {V:} {Endo-classes}},
     journal = {Documenta mathematica},
     pages = {23--77},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/360},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/360/}
}
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