Multiplicity-free homogeneous operators in the Cowen-Douglas class

2009/01/07 by Adam Korányi, Korányi, Adam, Gadadhar Misra +1 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #math.FA #math.RT

paper · pdf · doi:10.48550/arxiv.0901.0794

arxiv created 2009/01/07 · arxiv updated 2009/12/01

Abstract

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 Möb -- the Möbius group consisting of bi-holomorphic automorphisms of the unit disc \mathbbD. 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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