Examples related to the Sakellaridis-Venkatesh conjecture

Abstract: In this talk, I will introduce the Sakellaridis-Venkatesh conjecture on the decomposition of global period, and give examples related to this conjecture. More specifically, the cases $X = \mathrm{SO}(n-1) \backslash \mathrm{SO}(n)$ and $X = \mathrm{U}(2) \backslash \mathrm{SO}(5)$. In both cases, I will determine the Plancherel decompositions of $L^2(X_v)$, where $v$ is a local place. Then I will prove the local relative character identity. In the global setting, I will give the factorization of the global period of $X = \mathrm{SO}(n-1) \backslash \mathrm{SO}(n)$, where the local functional comes from the local Plancherel decomposition. The example $X = \mathrm{U}(2) \backslash \mathrm{SO}(5)$ is slightly beyond the SV conjecture but we still have a decomposition of the global period as the sum of two factorizable elements.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID: 646 0419 2446

Zoom password: 984662

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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