Berezin quantization and holomorphic representations
Berezin transform for non-scalar holomorphic discrete series
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...
Berezin-Weyl quantization for Cartan motion groups
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 spheres
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.
Bounded generation and Kazhdan’s property
Bounded orbits of flows on homogeneous spaces.
Branching theorems for semisimple Lie groups of real rank one