14/11/2013, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Abdelhamid Boussejra, Université Ibn Tofail, Kenitra, Morocco.
The Hua operators on homogeneous line bundles over bounded
symmetric domains of tube type
Let be a bounded symmetric domain of tube
type. We show that the image of the Poisson transform on the
degenerate principal series representation of attached to the
Shilov boundary of is characterized by a -
covariant differential operator on a homogeneous line bundle over
. As a consequence of our result we get the
eigenvalues of the Casimir operator for Poisson transforms on
homogeneous line bundles over . This extends a result of
Imemura and all on symmetric domains of classical type to all
symmetric domains. Also we compute a class of Hua type integrals
generalizing an earlier result of Faraut and Koranyi.