Academics

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

Time:2023-12-04 Mon 10:00-11:00

Venue:YMSC-C654 ZOOM:271 534 5558(PW: YMSC)

Organizer:Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu

Speaker:Jiandi Zou Technion

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.

Related News
    • 0

      Characteristic numbers, Jiang subgroup and non-positive curvature

      AbstractA sufficient condition in terms of Jiang subgroup is presented for the vanishing of signature and arithmetic genus. Along this line, some progress can be made on a question of Farrell and a complex version's Hopf conjecture

    • 1

      Categorified Quantum Groups, Braided Monoidal 2-Categories and the 4d Kitaev Model

      AbstractIt is well-known since the work of Hopf, Drinfel’d, Majid, Witten, and etc. in the late 20th century that Hopf algebra quantum groups play a signification role in both physics and mathematics. In particular, the category of representations of quantum groups are braided, and hence captures invariants of knots. This talk is based on works with F. Girelli, where we develop a systematic ca...