Symmetric power functoriality for modular forms

Abstract: Langlands functoriality predicts the transfer of automorphic representations along maps of L-groups. In particular, the symmetric power representation $\mathrm{Symm}^{n-1}$ of $\mathrm{GL}(2)$ should give rise to a lifting from automorphic representations of $\mathrm{GL}(2)$ to automorphic representations of $\mathrm{GL}(n)$. I will discuss joint work with Jack Thorne, in which we prove the existence of all symmetric power lifts for many cuspidal Hecke eigenforms (for example, those of square-free level).

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID = 616 2536 2002 ; PIN = 672097

---

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

---