Canonical and Boundary Representations on Rank One Para-Hermitian Spaces
- 1 G. R. Derzhavin Tambov State University, Tambov, Russia
Abstract
This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces G/H with G = SL( n ,R), H = GL( n -1,R) . For Hermitian symmetric spaces G/K , canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H , the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.
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