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Henrik Seppänen (Institutionen för matematiska vetenskaper, matematik)
International Journal of Mathematics (0129-167X). Vol. 19 (2008), 10, p. 1247-1268.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Lie groups, unitary representations, branching law, real bounded, symmetric domains, HOLOMORPHIC DISCRETE-SERIES, BOUNDED SYMMETRIC DOMAINS, TENSOR-PRODUCTS, ANALYTIC CONTINUATION, BRANCHING LAWS, TRANSFORM, SPACES

Denna post skapades 2009-10-22.
CPL Pubid: 100529


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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