Let B be an irreducible hermitian symmetric domain of rank r in ℂ d and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary ∂ B of B and of invariant differential operators acting on symmetric domains of lower rank.
Bibliographical noteFunding Information:
The authors gratefully acknowledge partial financial support by the Erwin-Schrö-dinger Institute (Vienna) and the German-Israeli-Foundation (GIF, grant No. I-415-023.06/95).
ASJC Scopus subject areas
- Algebra and Number Theory