Geodesic
Dualizing Involutions for Classical and Similitude Groups over Local Non-Archimedean Fields
Journal of Lie theory, Tome 27 (2017) no. 2, pp. 419-434 Cet article a éte moissonné depuis la source Heldermann Verlag

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Building on ideas of Tupan, we give an elementary proof of a result of Moeglin, Vignéras and Waldspurger on the existence of automorphisms of many p-adic classical groups that take each irreducible smooth representation to its dual. Our proof also applies to the corresponding similitude groups. It does not apply in even residual characteristic.
Classification : 22E50, 20G05
Mots-clés : Classical and similitude groups, involution, dual representation, Cayley maps 
@article{JLT_2017_27_2_JLT_2017_27_2_a6,
     author = {A. Roche and C. R. Vinroot},
     title = {Dualizing {Involutions} for {Classical} and {Similitude} {Groups} over {Local} {Non-Archimedean} {Fields}},
     journal = {Journal of Lie theory},
     pages = {419--434},
     year = {2017},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_2_JLT_2017_27_2_a6/}
}
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A. Roche; C. R. Vinroot. Dualizing Involutions for Classical and Similitude Groups over Local Non-Archimedean Fields. Journal of Lie theory, Tome 27 (2017) no. 2, pp. 419-434. http://geodesic.mathdoc.fr/item/JLT_2017_27_2_JLT_2017_27_2_a6/