In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...

Abstract. A general method for computing irreducible representations of Weyl groups and Iwahori-Hecke algebras was introduced by the first author in [8]. In that paper the representations of the algebras of types An, Bn, Dn and G2 were computed and it is the purpose of this paper to extend these computations to F4. The main goal here is to compute irreducible representations of the Iwahori-Heck...

The Fock space of m+p bosonic and n+q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm+p|n+q. Its tensor powers decompose into direct sums of infinite dimensional irreducible highest weight glm+p|n+q-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irredu...

We classify all finite groups G that possess an element x ∈ such every irreducible character of takes a root unity value at x.

We prove a closed character formula for the symmetric powers SNV (λ ) of a fixed irreducible representation V (λ ) of a complex semi-simple Lie algebra g by means of partial fraction decomposition. The formula involves rational functions in rank of g many variables which are easier to determine than the weight multiplicities of SNV (λ ) themselves. We compute those rational functions in some in...

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p > 0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it is now directly applicable to any dominant highest weight. 1. Let G be an almost simple, simply connected algebraic group over k, an algebraically closed ...

 ‎Let $V$ be an $n$-dimensional complex inner product space‎. ‎Suppose‎ ‎$H$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎Hrightarrow mathbb{C} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎Denote by $V_{chi}(H)$ the symmetry class‎ ‎of tensors associated with $H$ and $chi$‎. ‎Let $K(T)in‎ (V_{chi}(H))$ be the operator induced by $Tin‎ ‎text{End}(V)$‎. ‎Th...

We have seen that irreducible representations of a compact Lie group G can be constructed starting from a highest weight space and applying negative roots to a highest weight vector. One crucial thing that this construction does not easily tell us is what the character of this irreducible representation will be. The character would tell us not just which weights occur in the representation, but...

We classify partitions which are of maximal p-weight for all odd primes p. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.