Multiplicity-free homogeneous operators in the Cowen-Douglas class

Details Multiplicity-free homogeneous operators in the Cowen-Douglas class Multiplicity-free homogeneous operators in the Cowen-Douglas class

2009-01-07

arxiv.org/abs/0901.0794v1

Mathematics

Functional Analysis

Scientific paper

In a recent paper, the authors have constructed a large class of operators in the Cowen-Douglas class Cowen-Douglas class of the unit disc $\mathbb D$ which are {\em homogeneous} with respect to the action of the group M\"{o}b -- the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit disc $\mathbb{D}$. The {\em associated representation} for each of these operators is {\em multiplicity free}. Here we give a different independent construction of all homogeneous operators in the Cowen-Douglas class with multiplicity free associated representation and verify that they are exactly the examples constructed previously.

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