Toeplitz Operators on Fock Space over Cn with Invariant Symbols under the Action of the Unit Circle

The first goal of this paper is to find a representation of the Fock space on C-n in terms of the weighted Bergman spaces of the projective spaces CPn-1; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on CPn-1. Also, we study the C* algebras generated by Toeplitz operators where the symbols are taken from the following two families of functions: Firstly, the symbols depend on the moment map associated with the unit circle, and secondly, the symbols are invariant under the same action. Moreover, we analyze the commutative relations between these algebras, and we apply these results to find new commutative Banach algebras generated by Toeplitz operators on Fock space of C-n.