Rodier type theorem for generalized principal series
Artikel i vetenskaplig tidskrift, 2021

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(IndPG(ρ)) of Jordan–Hölder constituents of the Harish-Chandra parabolic induction representation IndPG(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 = N (M) / M is not a coxeter group in general, as opposed to the well-known fact that the Weyl group W = N (T) / T is a coxeter group. Along the way, we sort out all regular discrete series/tempered/generic representations for arbitrary G, generalizing Tadić’s work on regular discrete series representation for split (G) Sp and SO , and also providing a new simple proof of Casselman–Shahidi’s theorem on generalized injectivity conjecture for regular generalized principal series. Indeed, such a beautiful structure theorem also holds for finite central covering groups. M G T G 2 n 2 n + 1

Regular supercuspidal representation

Generalized principal series

Generic

Discrete series

Tempered representation

Författare

Caihua Luo

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1007/s00209-021-02723-9

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Senast uppdaterat

2021-04-15