Iwahori-Hecke algebras for the infinite series of complex reflection groups G(r, p, n) were constructed recently in the work of Ariki and Koike [AK], Broué and Malle [BM], and Ariki [Ari]. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper [HR] in which we derived Murnagha...

Some problems concerning the decomposition of certain characters of SL( n, C) are studied from a combinatorial point of view. The specific characters considered include those of the exterior and symmetric algebras of the adjoint representation and the Euler characteristic of Hanlon's so-called "Macdonald complex." A general recursion is given for computing the irreducible decomposition of these...

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters.

Kronecker products of complex characters of the symmetric group Sn have been studied in many papers. Information on special products and on the coefficients of special constituents have been obtained but there is no efficient combinatorial algorithm in sight for computing these products. In [1], products of Sn-characters with few homogeneous components and homogeneous products of characters of ...

Irreducible characters of Hecke algebras of type A may be represented as reened counts of simple statistics on suitable subsets of permutations. Such formulas have been generalized to characters of other Coxeter groups and their Hecke algebras and to coinvariant algebras. In this paper we present several formulas, applications to combinatorial identities, and related problems. New results are g...

We compute the irreducible constituents of the restrictions of all unipotent characters of the groups Sp4(q) and Sp6(q) and odd q to their maximal parabolic subgroups stabilizing a line. It turns out that these restrictions are multiplicity free. We also obtain general information about the restrictions of Harish-Chandra induced characters.

In 1980, Lusztig posed the problem of showing the existence of a unipotent support for the irreducible characters of a finite group of Lie type. This problem was solved by Lusztig in the case where the characteristic of the field over which the group is defined is large enough. The first named author extended this to the case where the characteristic is good. It is the purpose of this paper to ...

We investigate the problem of finding a set of prime divisors of the order of a finite group, such that no two irreducible characters are in the same p-block for all primes p in the set. Our main focus is on the simple and quasisimple groups. For results on the alternating and symmetric groups and their double covers, some combinatorial results on the cores of partitions are proved, which may b...

Abstract We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on characteristic we also prove a gap result showing that next larger have degree roughly square of those non-trivial characters.

The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identificati...