Abstract
We prove that Toeplitz operators, acting on the pluriharmonic Bergman space of the Siegel domain, generate commutative \(C^*\)- algebras in the following two cases: when the class of symbols are invariant functions under the action of the quasi-parabolic group of biholomorphisms of the Siegel domain and when the class of symbols consists of all invariant functions under the action of the nilpotent group of biholomorphisms of the Siegel domain.
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