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 1247-1268Subject Categories
Mathematics
DOI
10.1142/S0129167X08005114