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Supercuspidal representations of GLn(F) distinguished by an orthogonal subgroup

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

邹建迪

时间

2023年12月04日 10:00 至 11:00

地点

Shuangqing-C654

线上

Zoom 271 534 5558 (YMSC)

摘要

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.