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BIMSA-YMSC Tsinghua Number Theory Seminar
Supercuspidal representations of GLn(F) distinguished by an orthogonal subgroup
Supercuspidal representations of GLn(F) distinguished by an orthogonal subgroup
Organizers
Hansheng Diao
, Yueke Hu
, Emmanuel Lecouturier
,
Cezar Lupu
Speaker
Jiandi Zou
Time
Monday, December 4, 2023 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
Online
Zoom 271 534 5558
(YMSC)
Abstract
Let F be a non-archimedean locally compact field of residue characteristic p \neq 2, let G = GLn(F) and let H be an orthogonal subgroup of G. For π a complex smooth supercuspidal representation of G, we give a full characterization for the distinguished space Hom_H(π, 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 π 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 π evaluating at −1 is 1.