Homogeneous Hermitian holomorphic vector bundles and operators in the Cowen-Douglas class over the poly-disc

A Family of Homogeneous Operators In The Cowen-Douglas Class Over The Poly-disc

“…In this paper, the group G is fixed once for all to be the subgroup Möb n of the group of bi-holomorphic automorphisms of D n . Moreover, it follows from Theorem 4.1 in [5] that the universal covering group Möb n acts on E M * uniquely by isometric bundle automorphisms. Also, we recall from [5, Section 4] that the homogeneity of…”

“…In the recent paper [5], all irreducible n -tuples in B r (D n ), r = 1, 2, 3, homogeneous with respect to the group Möb n (respectively, Aut(D n )) have been listed modulo unitary equivalence. It has been also noted, in the same article, that the representations associated to the n -tuples of operators in B r (D n ) homogeneous with respect to Möb n , r = 1, 2, 3, must be multiplicity-free.…”

“…, Tn−1 , Ŝ) are the only irreducible n -tuples of operators (up to unitary equivalence) in B r (D n ), r = 1, 2, homogeneous with respect to Möb n (cf. [5,Theorem 3.1,Theorem 6.7]).…”

A family of homogeneous operators in the Cowen–Douglas class over the poly-disc

“…In the recent paper [5], all irreducible n-tuples in B r (D n ), r = 1, 2, 3, homogeneous with respect to the group Möb n (respectively, Aut(D n )) have been listed modulo unitary equivalence. It has also been noted in [5] that the representations associated to n-tuples of operators in B r (D n ) homogeneous with respect to Möb n , r = 1, 2, 3, must be multiplicity-free.…”

“…, Tn−1 , Ŝ) are the only irreducible n-tuples of operators (up to unitary equivalence) in B r (D n ), r = 1, 2, homogeneous with respect to Möb n (cf. [5,Theorems 3.1,6.7]).…”