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arXiv · 2105.14235

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

Nahid Walji
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Abstract

Given a cuspidal automorphic representation $\pi$ for GL(3) over a number field and a positive integer $k$, assume that the symmetric $m$th power lifts of $\pi$ are isobaric automorphic for $m \leq k$, cuspidal for $m \leq k-1$, and that certain associated Rankin-Selberg products are isobaric automorphic. Then the number of cuspidal isobaric summands in the $k$th symmetric power lift is bounded above by 3 when $k \geq 7$, and bounded above by 2 when $k \geq 19$ with $k \equiv 1 \pmod 3$. We then investigate the analogous problem for GL(4).

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Nahid Walji. 2021-05-29. On the conjectural decomposition of symmetric powers of automorphic representations for GL(3) and GL(4). https://arxiv.org/abs/2105.14235

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