A very easy approach to the holomorphic discrete series
Based on the material in an old article of Wallach a short proof of the Harish-Chandra condition is given.
math.RT↗
arXiv subjects
Adam Korányi
Publications and source records attributed to Adam Korányi.
Multiplicity-free homogeneous operators in the Cowen-Douglas class
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 $\mathbb{D}$. 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.
math.FA↗
A unified approach to compact symmetric spaces of rank one
A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.
math.DG↗
Homogeneous operators on Hilbert spaces of holomorphic functions -- I
In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the Möbius group consisting of bi-holomorphic automorphisms of the unit disc $\mathbb D$. For every $m \in \N$ we have a family of operators depending on $m+1$ positive real parameters. The kernel function is calculated explicitly. It is proved that each of these operators is bounded, lies in the Cowen-Douglas class of $\mathbb D$ and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent.
math.FA↗