Abstract The codegree of an irreducible character $\chi $ a finite group G is $|G : \ker \chi |/\chi (1)$ . We show that the Ree ${}^2G_2(q)$ , where $q = 3^{2f+1}$ determined up to isomorphism by its set codegrees.

The Lie algebra D̂, which is the unique non-trivial central extension of the Lie algebra D of differential operators on the circle [KP1], has appeared recently in various models of two-dimensional quantum field theory and integrable systems, cf., e.g., [BK, FKN, PRS, IKS, CTZ, ASvM]. A systematic study of representation theory of the Lie algebra D̂, which is often referred to as W1+∞ algebra, was...

How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers ; and there remain practical difficulties even for groups of relatively small orders ( á 100). The present ...

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...

Let G be an algebraic group over an algebraically closed field k of characteristic p > 0. In this paper we develop the theory of character sheaves on groups G such that their neutral connected components G◦ are solvable algebraic groups. For such algebraic groups G (which we call neutrally solvable) we will define the set CS(G) of character sheaves on G as certain special (isomorphism classes o...

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

Let Fq be a finite field with q elements, where q is the power of an odd prime, and let GSp(2n, Fq) and GO±(2n, Fq) denote the symplectic and orthogonal groups of similitudes over Fq, respectively. We prove that every real-valued irreducible character of GSp(2n, Fq) or GO±(2n, Fq) is the character of a real representation, and we find the sum of the dimensions of the real representations of eac...

Given a knot K in an integral homology sphere Σ with exterior NK , there is a natural action of the cyclic group Z/n on the space of SL(n,C) representations of the knot group π1(NK), and this induces an action on the SL(n,C) character variety Xn(NK). We identify the fixed points of this action in X ∗ n(NK) with characters of irreducible metabelian representations. We then show that for any irre...