Toeplitz operators on Jordan–Kepler varieties

Abstract

We study Toeplitz operators on Hilbert spaces of holomorphic functions on algebraic varieties, the generalized Kepler varieties defined in Jordan theoretic terms. Using the fine analysis of the reproducing kernel function, we construct and classify the irreducible representations of the $C^{\ast }$-algebra generated by these operators (with smooth symbols). The limit behavior of Bergman-type measures under peaking functions is of special importance.