In 1998, the second author raised the problem of classifying the irreducible characters of Sn of prime power degree. Zalesskii proposed the analogous problem for quasi-simple groups, and he has, in joint work with Malle, made substantial progress on this latter problem. With the exception of the alternating groups and their double covers, their work provides a complete solution. In this article...

We give new evidence to the fact that structure of a solvable group can be controlled by irreducible monomial characters. In particular, we inspect role characters in Isaacs–Navarro–Wolf conjecture and Gluck’s conjecture.

The present paper is a survey of a simple combinatorial model for the irreducible characters of complex semisimple Lie algebras, and, more generally, of complex symmetrizable Kac-Moody algebras. This model, which will be referred to as the alcove path model, can be viewed as a discrete counterpart to the Littelmann path model. It allows us to give character formulas and a LittlewoodRichardson r...

The W3 algebra of central charge 6/5 is realized as a subalgebra of the vertex operator algebra V2A2 associated with a lattice of type √ 2A2 by using both coset construction and orbifold theory. It is proved that W3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.

Much can be learned about a finite group from its character table, but sometimes that table can be difficult to compute. Supercharacter theories are generalizations of character theory, defined by P. Diaconis and I.M. Isaacs in [8], in which certain (possibly reducible) characters called supercharacters take the place of the irreducible characters, and a certain coarser partition of the group t...

We study the level-one irreducible highest weight representations of Uq[ ̂ gl(1|1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated. Mathematics Subject Classifications (1991): 17B37, 81R10, 81R50, 16W30

We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra Uq[ ̂ gl(N |N)]. We study in details the level-one irreducible highest weight representations of Uq[ ̂ gl(2|2)], and compute the characters and supercharacters associated with these irreducible modules. Mathematics Subject Classifications (1991): 17B37, 81R50, 81R10, 16W30