论文信息 - Noncommutative Cyclic Characters of Symmetric Groups

Noncommutative Cyclic Characters of Symmetric Groups

We define noncommutative analogues of the characters of the symmetric group which are induced by transitive cyclic subgroups (cyclic characters). We investigate their properties by means of the formalism of noncommutative symmetric functions. The main result is a multiplication formula 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 multiplicative property of the major index of permutations.

[1] Alain Lascoux,et al. Noncommutative symmetric functions , 1994 .

[2] J. Shaw. Combinatory Analysis , 1917, Nature.

[3] J. Thibon,et al. A Hopf-Algebra Approach to Inner Plethysm , 1994 .

[4] Israel M. Gelfand,et al. Noncommutative Symmetrical Functions , 1995 .

[5] Gérard Henry Edmond Duchamp,et al. Déformations de projecteurs de Lie , 1994 .

[6] I. Gel'fand,et al. A theory of noncommutative determinants and characteristic functions of graphs , 1992 .

[7] Louis Solomon,et al. A Mackey formula in the group ring of a Coxeter group , 1976 .

[8] John R. Stembridge,et al. ON THE EIGENVALUES OF REPRESENTATIONS OF REFLECTION GROUPS AND WREATH PRODUCTS , 1989 .

[9] Alain Lascoux,et al. Green Polynomials and Hall-Littlewood Functions at Roots of Unity , 1994, Eur. J. Comb..

[10] J. Plebański,et al. Combinatorial approach to Baker-Campbell-Hausdorff exponents , 1970 .

[11] A. Klyachko. Lie elements in the tensor algebra , 1974 .

[12] I. G. MacDonald,et al. Symmetric functions and Hall polynomials , 1979 .

[13] I. Gel'fand,et al. Determinants of matrices over noncommutative rings , 1991 .

[14] I. Gessel. Multipartite P-partitions and inner products of skew Schur functions , 1983 .