Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three

Abstract

We use the combinatorial way to give an explicit expression for the product of the class of cycles of length three with an arbitrary class of cycles. In addition, an explicit formula for the coefficient of an arbitrary class in the expansion of the product of an arbitrary class by the class of cycles of length three is given.

Keywords

• The center of the symmetric group algebra,Structure coefficients,Product of conjugacy classes of the symmetric group,Representation theory of the symmetric group

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