On the conjectural decomposition of symmetric powers of automorphic representations for GL(3) and GL(4)

Nahid Walji (University of British Columbia)

20-May-2021, 21:00-22:00 (3 years ago)

Abstract: Let $\Pi$ be a cuspidal automorphic representation for GL(3) over a number field. We fix an integer $k \geq 2$ and we assume that the symmetric $m$th power lifts of $\Pi$ are automorphic for $m \leq k$, cuspidal for $m < k$, and that certain associated Rankin–Selberg products are automorphic. In this setting, we bound the number of cuspidal isobaric summands in the $k$th symmetric power lift. In particular, we show it is bounded above by 3 for $k \geq 7$, and bounded above by 2 when $k \geq 19$ with $k$ congruent to 1 mod 3. We will also discuss the analogous problem for GL(4).

number theory

Audience: researchers in the topic

Comments: This will include a pre-talk.


UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

Organizers: Kiran Kedlaya*, Alina Bucur, Aaron Pollack, Cristian Popescu, Claus Sorensen
*contact for this listing

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