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- W3100984695 abstract "Let $F$ be a non-archimedean locally compact field of residue characteristic $pneq2$, let $G=mathrm{GL}_{n}(F)$ and let $H$ be an orthogonal subgroup of $G$. For $pi$ a complex smooth supercuspidal representation of $G$, we give a full characterization for the distinguished space $mathrm{Hom}_{H}(pi,1)$ being non-zero and we further study its dimension as a complex vector space, which generalizes a similar result of Hakim for tame supercuspidal representations. As a corollary, the embeddings of $pi$ in the space of smooth functions on the set of symmetric matrices in $G$, as a complex vector space, is non-zero and of dimension four, if and only if the central character of $pi$ evaluating at $-1$ is $1$." @default.
- W3100984695 created "2020-11-23" @default.
- W3100984695 creator A5029258145 @default.
- W3100984695 date "2020-11-14" @default.
- W3100984695 modified "2023-09-26" @default.
- W3100984695 title "Supercuspidal representations of $mathrm{GL}_{n}(F)$ distinguished by an orthogonal involution" @default.
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- W3100984695 doi "https://doi.org/10.48550/arxiv.2011.07349" @default.
- W3100984695 hasPublicationYear "2020" @default.
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