28 research outputs found
Hua operators, Poisson transform and relative discrete series on line bundle over bounded symmetric domains
Let be a bounded symmetric domain and its Shilov
boundary. We consider the action of on sections of a homogeneous line
bundle over and the corresponding eigenspaces of -invariant
differential operators. The Poisson transform maps hyperfunctions on the to
the eigenspaces. We characterize the image in terms of twisted Hua operators.
For some special parameters the Poisson transform is of Szeg\"o type mapping
into the relative discrete series; we compute the corresponding elements in the
discrete series
Jordan algebras, geometry of Hermitian symmetric spaces and non-commutative Hardy spaces
These notes were written following lectures I had the pleasure of giving on
this subject at Keio University, during November and December 2004. The first
part is about new applications of Jordan algebras to the geometry of Hermitian
symmetric spaces and to causal semi-simple symmetric spaces of Cayley type. The
second part will present new contributions for studing (non commutative) Hardy
spaces of holomorphic functions on Lie semi-groups which is a part of the so
called Gelfand-Gindikin program
Conformally Covariant Bi-Differential Operators on a Simple Real Jordan Algebra
For a simple real Jordan algebra a family of bi-differential operators
from to is constructed.
These operators are covariant under the rational action of the conformal group
of They generalize the classical {\em Rankin-Cohen} brackets (case
)
The Schwarzian derivative on symmetric spaces of Cayley type
International audienceLet M be a symmetric space of Cayley type. For any conformal diffeomorphism of M we study the relationship betwenn the conformal factor of f and a generalized Schwarzian derivative of f
THE SCHWARZIAN DERIVATIVE ON SYMMETRIC SPACES OF CAYLEY TYPE
International audienceLet M be a symmetric space of Cayley type and f a conformal diffeomorphism of M. We study a relationship between the conformal factor of f and a generalized Shwarzian derivatine of f
The source operator method: an overview
This is an overview on the {source operator method} which leads to the
construction of symmetry breaking differential operators (SBDO) in the context
of tensor product of two principals series representations for the conformal
group of a simple real Jordan algebra. This method can be applied to other
geometric contexts: in the construction of SBDO for differential forms and for
spinors, and also for the construction of Juhl's operators corresponding to the
restriction from the sphere to