Rodier type theorem for generalized principal series

2019/03/16 by Luo, Caihua
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1903.06887

Abstract

Given a regular supercuspidal representation ρ of the Levi subgroup M of a standard parabolic subgroup P=MN in a connected reductive group G defined over a non-archimedean local field F, we serve you a Rodier type structure theorem which provides us a geometrical parametrization of the set JH(Ind^G_P(ρ)) of Jordan--Hölder constituents of the Harish-Chandra parabolic induction representation Ind^G_P(ρ), vastly generalizing Rodier structure theorem for P=B=TU Borel subgroup of a connected split reductive group about 40 years ago. Our novel contribution is to overcome the essential difficulty that the relative Weyl group W_M=N_G(M)/M is not a coxeter group in general, as opposed to the well-known fact that the Weyl group W_T=N_G(T)/T is a coxeter group. Indeed, such a beautiful structure theorem also holds for finite central covering groups.

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