Mathematics – Representation Theory
Scientific paper
2007-03-27
Mathematics
Representation Theory
Scientific paper
In this paper we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from $Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to $GL(n,\mathbb{C})$ respectively. We work with the realisations 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.
No associations
LandOfFree
Tube domains and restrictions of minimal representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Tube domains and restrictions of minimal representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tube domains and restrictions of minimal representations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-372881