For a long time now, I have tried to look for the representation theory of $SO(p,q)$. I am in particular interested in the unitary irreducible representations and the bilinear Hermitian form on the space of (homogeneous) functions. I know that for certain degrees, the representations are unitary, but I want to know the associated bilinear form. Any reference (other then Vilenkin for $SL(2,\mathbf{R})$) would be welcome :)
2026-03-30 20:42:37.1774903357
Representation theory of SO(p,q)
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Infinite dimensional unitary representations of $SO(p,q)$ are discussed in section 9.2.9, 9.2.10 of the book
N.Vilenkin and A.Klimyk "Representations of Lie groups and special functions", Volume 2, Kluwer, 1993.