An F. and M. Riesz theorem for compact Lie groups.
Let be a Hermitian symmetric space of the non-compact type and let be a discrete series representation of which is holomorphically induced from a unitary irreducible representation of . In the paper [B. Cahen, Berezin quantization for holomorphic discrete series representations: the non-scalar case, Beiträge Algebra Geom., DOI 10.1007/s13366-011-0066-2], we have introduced a notion of complex-valued Berezin symbol for an operator acting on the space of . Here we study the corresponding...
We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].
BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called -types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.