Toeplitz $C^*$-Algebras on Boundary Orbits of Symmetric Domains

TL;DR

This paper classifies irreducible representations of Toeplitz $C^*$-algebras on symmetric domain boundary orbits, using hypergeometric measures and peaking functions to analyze their structure.

Contribution

It provides a classification of irreducible representations of Toeplitz $C^*$-algebras on boundary orbits of symmetric domains, extending understanding of their structure.

Findings

Classification of irreducible representations of Toeplitz $C^*$-algebras

Analysis of hypergeometric measures under peaking functions

Insights into boundary orbit structures of symmetric domains

Abstract

We study Toeplitz operators on Hilbert spaces of holomorphic functions on symmetric domains, and more generally on certain algebraic subvarieties, determined by integration over boundary orbits of the underlying domain. The main result classifies the irreducible representations of the Toeplitz $C^*$-algebra generated by Toeplitz operators with continuous symbol. This relies on the limit behavior of "hypergeometric" measures under certain peaking functions.