The Howe-Moore property for real and $p$-adic groups

Moore groups have the WS-property

Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups

‎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 w...

p-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...

SIMPLE p - ADIC GROUPS , II

0.1. For any finite group Γ, a “nonabelian Fourier transform matrix” was introduced in [L1]. This is a square matrix whose rows and columns are indexed by pairs formed by an element of Γ and an irreducible representation of the centralizer of that element (both defined up to conjugation). As shown in [L2], this matrix, which is unitary with square 1, enters (for suitable Γ) in the character for...

Twisted signs for p-adic linear groups

Let G be a reductive p-adic group and let θ be an automorphism of G of order at most two. Let π be an irreducible smooth representation of G that is taken to its dual by θ. The space V of π then carries a non-zero bilinear form ( , ) ( unique up to scaling) with the invariance property (π(g)v, π(g)w) = (v, w), for g ∈ G and v, w ∈ V . The form is easily seen to be symmetric or skew-symmetric an...