Arithmetic and Representation Theory (ART) Seminar

Abstract: In this talk, we will use type theory to construct a family of depth 1/N supercuspidal representations of p-adic GL(2N, F) which we call middle supercuspidal representations. These supercuspidals may be viewed as a natural generalization of simple supercuspidal representations, i.e. those supercuspidals of minimal positive depth. Via explicit computations of twisted gamma factors, we will show that middle supercuspidal representations may be uniquely determined through twisting by quasi-characters of F* and simple supercuspidal representations of GL(N, F). Furthermore, we will pose a conjecture which refines the Local Converse Theorem for GL(n, F).