TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Lie groups

unitary representations

branching law

real bounded

symmetric domains

HOLOMORPHIC DISCRETE-SERIES

BOUNDED SYMMETRIC DOMAINS

TENSOR-PRODUCTS

ANALYTIC CONTINUATION

BRANCHING LAWS

TRANSFORM

SPACES

symmetric domains

Publication and Content Type

ref (subject category)

art (subject category)