NONCOMMUTATIVE CYCLIC CHARACTERS OF SYMMETRICAL GROUPS

We define noncommutative analogues of the characters of the symmetric group which are induced by transitive cyclic subgroups (cyclic charact ers). We investigate their properties by means of the formalism of non commutative symmetric functions. The main result is a multiplication f ormula whose commutative projection gives a combinatorial formula for the resolution of the Kronecker product of two cyclic representations of the symmetric group. This formula can be interpreted as a multiplic ative property of the major index of permutations. (C) 1996 Academic P ress, Inc.