Semisimple characters for inner forms II: Quaternionic forms of 𝑝-adic classical groups (𝑝 odd)

Skodlerack, Daniel

doi:10.1090/ert/544

Semisimple characters for inner forms II: Quaternionic forms of $p$-adic classical groups ($p$ odd)
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Represent. Theory 24 (2020), 323-359 Request permission

Abstract:

In this article we consider the set $G$ of rational points of a quaternionic form of a symplectic or an orthogonal group defined over a non-Archimedean local field of odd residue characteristic. We construct all full self-dual semisimple characters for $G$ and we classify their intertwining classes using endo-parameters. We compute the set of intertwiners between self-dual semisimple characters, and prove an intertwining and conjugacy theorem. Finally we count all $G$-intertwining classes of full self-dual semisimple characters which lift to the same $\tilde {G}$-intertwining class of a full semisimple character for the ambient general linear group $\tilde {G}$ for $G$.

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