2023/01/24 by Chan, Charlotte, Oi, Masao
#11F70 #FOS: Mathematics #Number Theory (math.NT) #Primary: 22E50 #Representation Theory (math.RT) #Secondary: 11S37
paper · doi:10.48550/arxiv.2301.09812
We prove that regular supercuspidal representations of p-adic groups are uniquely determined by their character values on very regular elements -- a special class of regular semisimple elements on which character formulae are very simple -- provided that this locus is sufficiently large. As a consequence, we resolve a question of Kaletha by giving a description of Kaletha's L-packets of regular supercuspidal representations which mirrors Langlands' construction for real groups following Harish-Chandra's characterization theorem for discrete series representations. Our techniques additionally characterize supercuspidal representations in general, giving p-adic analogues of results of Lusztig on reductive groups over finite fields. In particular, we establish an easy, non-cohomological characterization of unipotent supercuspidal representations when the residue field of the base field is sufficiently large.