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Polarizable Theta-Stable Parabolic Subalgebras and K-Saturation in the Non-compact Real Forms of G2 and F4

  • Steven Glenn Jackson
  • Alfred G. Noël
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)

Abstract

A general method for finding theta-stable parabolic subalgebras 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 -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.

Keywords

Conjugacy Class Simple Root Nilpotent Orbit Root Space Complex Span 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Steven Glenn Jackson
    • 1
  • Alfred G. Noël
    • 1
  1. 1.Department of MathematicsUniversity of Massachusetts BostonUSA

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