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)


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.


Conjugacy Class Simple Root Nilpotent Orbit Root Space Complex Span 
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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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