Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups
Authors
Abstract:
We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups. We prove Arthur's conjecture, the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group, for quasi-split special unitary groups and their inner forms. Furthermore, we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms. This work is applied to transferring known results in the second-named author's earlier work for quasi-split special unitary groups to their non-quasi-split inner forms.
similar resources
THE UNITARY I–SPHERICAL DUAL FOR SPLIT p–ADIC GROUPS OF TYPE F4
It is known that the determination of the Iwahori-spherical unitary dual for p-adic groups can be reduced to the classification of unitary representations with real infinitesimal character for the associated Hecke algebras. In this setting, I determine the Iwahori–spherical unitary dual for split
full textREDUCIBILITY OF SOME INDUCED REPRESENTATIONS OF p-ADIC UNITARY GROUPS
In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to...
full textOn local gamma factors for orthogonal groups and unitary groups
In this paper, we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for irreducible admissible representations of orthogonal groups, or unitary groups. One family is that of local integrals of the doubling method, and the other family is that of local integrals expressed in terms of sph...
full textOn special representations of p–adic reductive groups
Let F be a non-Archimedean locally compact field, let G be a split connected reductive group over F . For a parabolic subgroup Q ⊂ G and a ring L we consider the G-representation on the L-module (∗) C∞(G/Q, L)/ ∑
full textp-adic Hurwitz groups
Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...
full textMy Resources
Journal title
volume 43 issue Issue 4 (Special Issue)
pages 117- 141
publication date 2017-08-30
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023