Principal representations of SO(p,p+1)

2011/08/16 by Véronique Fischer, Veronique Fischer, Fischer, Veronique +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research #math.RT #msc:22E46 #msc:43A80

paper · pdf · doi:10.48550/arxiv.1108.3338

15 pages

arxiv created 2012/06/14 · arxiv updated 2012/06/15

Abstract

For p odd, the Lie group SO₀(p+1,p+1) has a family of unitary degenerate principal series representations realized on the space of real (p+1) by (p+1) skew symmetric matrices, similar to the Stein's complementary series for SL(2n,C) or Speh's representation for SL(2n,R). We consider their restriction on the subgroup G= SO(p+1,p) and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of G, and also irreducible under a maximal parabolic subgroup of G.

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