Polarizable Theta-Stable Parabolic Subalgebras and K_C-Saturation in the Non-compact Real Forms of G_2 and F_4

摘要

A general method for finding theta-stable parabolic subalge-bras was given in 2004 . In this paper, we develop LiE subroutines to find representatives of conjugacy classes of polarizable theta-stable parabolic subalgebras. Using a theorem of Tauvel, we implement algorithms for computing the K_C-saturation of the nilradical of such parabolic subalgebras. Furthermore, we provide a tool for testing a long standing conjecture that relates the wave front set of a representation of a real or p-adic group to special nilpotent orbits. Incidently, the conjecture is true for classical groups.