Toeplitz C*-Algebras on Super-Cartan Domains

Abstract

We study Hilbert spaces of super-holomorphic functions (including anti-commuting Grassmann variables) in the setting of bounded symmetric domains, more precisely for the matrix ball of arbitrary size. Our main results concern the classication of irreducible representations of the associated Toeplitz C*- algebra and an explicit decomposition of the super-Bergman space as a direct sum of vector-valued (ordinary) Bergman spaces.