Generalized principal series representations of 𝑆𝐿(1+𝑛,ℂ)

Dooley, Anthony; Zhang, Genkai

doi:10.1090/S0002-9939-97-03877-X

Generalized principal series representations of $SL(1+n,\mathbb {C})$
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by Anthony H. Dooley and Genkai Zhang PDF

Proc. Amer. Math. Soc. 125 (1997), 2779-2787 Request permission

Abstract:

We consider certain induced representations of the group $SL(n+1, \mathbb {C})$ realized on line bundles over the projective space of $\mathbb {C}^{n+1}$. We calculate the intertwining operators in the compact picture. We find all the unitarizable representations and determine the invariant norm.

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