Noncommutative cyclic characters of symmetric groups (Q1919668)

This paper is based on the recent development of a theory of noncommutative symmetric functions (instead of being polynomials, these involve noncommuting indeterminates). There is a well-known connection between symmetric functions (also Schur-functions, descent algebras, etc.) and characters of symmetric groups. In particular, the characters induced by transitive cyclic subgroups (of a symmetric group) correspond to certain symmetric functions with a rich combinatorial structure, and this paper discusses analogues of those in the context of noncommutative symmetric functions. The main result is a multiplication formula for these noncommutative cyclic characters. The commutative projection of this formula gives a combinatorial formula for the Kronecker product of two cyclic representations of the symmetric group. The authors also give an interpretation of this formula as a multiplicative property of the major index of permutations.