Endoscopic lifting of simple supercuspidal representations of SO(2n+1) to GL(2n)

TL;DR

This paper computes characters of simple supercuspidal representations of twisted GL(2n) and SO(2n+1) over p-adic fields, establishing their liftings via endoscopic character relations assuming p ≠ 2.

Contribution

It explicitly determines the endoscopic liftings of simple supercuspidal representations from SO(2n+1) to GL(2n) over p-adic fields.

Findings

Characters of simple supercuspidal representations are computed.

Endoscopic character relations are used to identify liftings.

Liftings are explicitly determined under the assumption p ≠ 2.

Abstract

We compute the characters of simple supercuspidal representations of twisted GL(2n) and standard SO(2n+1) over a p-adic field. Comparing them by the endoscopic character relation, we determine the liftings of simple supercuspidal representations of SO(2n+1) to GL(2n), under the assumption that p is not equal to 2.