Abstract We present a description of non-solvable groups in which all real irreducible character degrees are prime-power numbers.

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2), using the values of the function as structure constants. The modules constructed using exponential-polynomial functions parameterise the irreducible objects of the category Õ of Chari with finite-dimensional homogeneous components. In this work, an expression for the formal character of su...

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2), using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realise the irreducible modules with finite-dimensional weight spaces in the category Õ of Chari. In this work, an expression for the formal character of such a module is...

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...

‎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 $tin‎ ‎text{end}(v)$‎. ‎the...

§1. Representations of finite groups 1 §1.1. Definition and Examples 1 §1.2. G-modules 3 §1.3. Mashke’s Theorem 4 §1.4. Schur’s Lemma 6 §1.5. One-dimensional representations 7 §1.6. Exercises 9 §2. Irreducible representations of finite groups 10 §2.1. Characters 10 §2.2. Basic operations on representations and their characters 11 §2.3. Schur’s orthogonality relations 12 §2.4. Decomposition of t...

In this paper we study the category C of finite–dimensional representations of affine Lie algebras. The irreducible objects of this category were classified and described explicitly in [2],[4]. It was known however that C was not semisimple. In such a case a natural problem is to describe the blocks of the category. The blocks of an abelian category are themselves abelian subcategories, each of...

A general method for computing irreducible representations of Weyl groups and Iwahori–Hecke algebras was introduced by the first author in [10]. In that paper the representations of the algebras of typesAn,Bn,Dn andG2 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–Hecke algebra of ...

In [APS17], the authors characterize the partitions of n whose corresponding representations of Sn have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups W . Namely, given a nontrivial multiplicative character ω of W , we give a closed formula for the number of irreducible representations of W with determinant ω. For Coxeter groups of type Bn a...

Computational methods for finding the character table of a finite group require a stock of reducible characters and techniques for decomposing these characters into irreducible characters. A method for generating reducible characters from a representation of a group is proposed. Several new techniques for computing the irreducible decompositions of a set of characters are given; these technique...