TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS
Journal article, 2008

In this paper, we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from Sp(n, R) to GL(+)(n, R), and from SU(n, n) to GL(n, C) respectively. We work with the realizations of the representation spaces as L-2-spaces on the boundary orbits of rank one of the corresponding cones, and give explicit integral operators that play the role of the intertwining operators for the decomposition. We prove inversion formulas for dense subspaces and use them to prove the Plancherel theorem for the respective decomposition. The Plancherel measure turns out to be absolutely continuous with respect to the Lebesgue measure in both cases.

symmetric domains

TENSOR-PRODUCTS

BOUNDED SYMMETRIC DOMAINS

TRANSFORM

real bounded

branching law

ANALYTIC CONTINUATION

SPACES

Lie groups

HOLOMORPHIC DISCRETE-SERIES

BRANCHING LAWS

unitary representations

Author

Henrik Seppänen

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

International Journal of Mathematics

0129-167X (ISSN)

Vol. 19 10 1247-1268

Subject Categories

Mathematics

DOI

10.1142/S0129167X08005114

More information

Created

10/6/2017