Endoscopic lifting of simple supercuspidal representations of unramified U(N) to GL(N)

TL;DR

This paper computes characters of simple supercuspidal representations of U(N) and twisted GL(N), and determines their liftings via endoscopic character relations, assuming p ≠ 2, advancing understanding of representation transfer in p-adic groups.

Contribution

It explicitly determines the endoscopic liftings of simple supercuspidal representations from U(N) to GL(N) for unramified cases, providing new insights into the local Langlands correspondence.

Findings

Computed characters of simple supercuspidal representations

Established endoscopic character relations for these representations

Determined explicit liftings from U(N) to GL(N)

Abstract

Let U(N) be the quasi-split unitary group in N variables for a quadratic unramified extension of p-adic fields. We compute the characters of simple supercuspidal representations of twisted GL(N) and U(N). Comparing them by the endoscopic character relation, we determine the liftings of simple supercuspidal representations of U(N) to GL(N), under the assumption that p is not equal to 2.