TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS
Artikel i vetenskaplig tidskrift, 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

Författare

Henrik Seppänen

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

International Journal of Mathematics

0129-167X (ISSN)

Vol. 19 1247-1268

Ämneskategorier

Matematik

DOI

10.1142/S0129167X08005114