Spin characters of generalized symmetric groups

Schur Q-functions and spin characters of symmetric groups I

In a classic paper, I. Schur [6] introduced a class of symmetric functions, now called Schur Qfunctions, in order to determine the irreducible spin (projective) characters of symmetric groups. In the case of the ordinary characters of symmetric groups, going back to the early work of D. E. Littlewood and A. R. Richardson [3], the corresponding Schur functions have been used to give useful combi...

Generalized Characters of the Symmetric Group

Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diag S(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand ...

Noncommutative Cyclic Characters of Symmetric Groups

We deene 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 c...

On Kronecker Products of Spin Characters of the Double Covers of the Symmetric Groups

In recent years, a number of results on Kronecker products of complex Sncharacters have been obtained. In particular, the rectangular hull for the constituents in such products was found, and this was used for the classification of products with few homogeneous components; see [1] for this classification result and references to related work. Here, we provide similar results for products of spi...

Spin modules for symmetric groups