Hardy spaces on two-sheeted covering semigroups.
Branching laws for some unitary representations of .
The geometry of nilpotent coadjoint orbits of convex type in hermitian Lie algebras.
Analytic continuation for Flensted-Jensen Representations.
L...-versions of the Howe correspondence I.
Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program
For the scalar holomorphic discrete series representations of and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside . We construct a Cayley transform between the Ol’shanskiĭ semigroup having as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for . This allows calculating the composition series in terms of harmonic analysis on . In particular we show that the Ol’shanskiĭ Hardy space for is different...
A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform
In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the -continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is -continuous for
Conformal indices of riemannian manifolds
Conformally invariant trilinear forms on the sphere
To each complex number is associated a representation of the conformal group on (spherical principal series). For three values , we construct a trilinear form on , which is invariant by . The trilinear form, first defined for in an open set of is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.
Conal Heisenberg algebras and associated Hilbert spaces.
Relative discrete series of line bundles over bounded symmetric domains
We study the relative discrete series of the -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.
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