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Semisimple characters for inner forms II: Quaternionic inner forms of classical groups

Year: 2017
Type: preprint
Abstract: In this article we consider a quaternionic inner form $G$ of a $p$-adic classical group defined over a non-archimedian 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. Further we prove an intertwining and conjugacy theorem for self-dual semisimple characters. We give the formulas for the set of intertwiners between self-dual semisimple characters. We count all $G$-intertwining classes of self-dual semisimple characters which lift to the same $\tilde{G}$-intertwining class of a semisimple character for the ambient general linear group $\tilde{G}$ for $G$.
DOI: 10.48550/arxiv.1801.00265
Language: English
Open Access status: green
Award: G289146336
OpenAlex ID: W2781998654
Cites: 9
Cited by: 1
Related to: 10