On stability for exterior and symmetric square for ${\rm GL}(n)$

Abstract: In local to global arguments, it is very useful to know the behaviour of $L$ and epsilon factors under very ramified twists. For GL$(n, F)$, $F$ local non-archimedean, Cogdell, Shahidi and Tsai proved that if one twists a given cuspidal representation $\pi$ with a ramified enough character, then the $L$ and epsilon factors for the exterior and symmetric square acquire a simple shape. They establish that ``stability" property, mainly by a local, intricate proof. We propose a global to local proof, taking advantage of progress in the global Langlands correspondence for GL$(n)$ over number fields.

number theoryrepresentation theory

Audience: researchers in the topic

Number Theory and Representations in Valparaiso