217 research outputs found
Homogeneous Vector Bundles and intertwining Operators for Symmetric Domains
The main features of homogeneous Cowen-Douglas operators, well-known for the
unit disk, are generalized to the setting of hermitian bounded symmetric
domains of arbitrary rank
A classification of homogeneous operators in the Cowen-Douglas class
A complete list of homogeneous operators in the Cowen-Douglas class
is given. This classification is obtained from an explicit realization of all
the homogeneous Hermitian holomorphic vector bundles on the unit disc under the
action of the universal covering group of the bi-holomorphic automorphism group
of the unit disc
Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains
It is known that all the vector bundles of the title can be obtained by
holomorphic induction from representations of a certain parabolic group on
finite dimensional inner product spaces. The representations, and the induced
bundles, have composition series with irreducible factors. We give a condition
under which the bundle and the direct sum of its irreducible constituents are
intertwined by an equivariant constant coefficient differential operator. We
show that in the case of the unit ball in this condition is
always satisfied. As an application we show that all homogeneous pairs of
Cowen-Douglas operators are similar to direct sums of certain basic pairs
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