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

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 $m\le k$, cuspidal for $m\le k-1$, 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 $k\ge 7$, and bounded above by 2 when $k\ge 19$ with $k\equiv 1(\mathrm{mod}3)$. We then investigate the analogous problem for GL(4).

18 pages. Comments welcome

References in corpus (1)

• A Cuspidality Criterion for the Exterior Square Transfer of Cusp Forms on GL(4)