Our goal is to describe factorizations of the characters of irreducible representations of compact semisimple Lie groups. It is well-known that for a given Lie group G of rank n, the Virtual Representation Ring R(G) with the operations of tensor product, direct sum, and direct difference is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, R...

An explicit character formula is established for any strongly generic finite-dimensional irreducible g-module, g being an arbitrary finite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible finite-dimensional g-module, i.e. such that its highest weight is far enough from the walls of the Weyl cha...

We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label the irreducible characters appearing as summands of the characters of Foulkes modules. The homomorphisms are defined using certain families of subsets of the na...

1. Let k be an algebraic closure of a finite field Fq. Let G = GLn(k). The group G(Fq) = GLn(Fq) can be regarded as the fixed point set of the Frobenius map F : G −→ G, (gij) 7→ (g q ij). Let Q̄l be an algebraic closure of the field of l-adic numbers, where l is a prime number invertible in k. The characters of irreducible representations of G(Fq) over an algebraically closed field of characteri...

In a previous work, the second-named author gave complete description of action automorphisms on ordinary irreducible characters finite symplectic groups. We generalise this in two directions. Firstly, using work first-named author, we give Galois characters. Secondly, extend both descriptions to cover case special orthogonal As consequence, obtain explicit for character fields and

Suppose that G is a …nite solvable group which has an irreducible character which vanishes on exactly one conjugacy class. Then we show that G has a homomorphic image which is a nontrivial 2-transitive permutation group. The latter groups have been classi…ed by Huppert. We can also say more about the structure of G depending on whether is primitive or not. Mathematics Subject Classi…cation 2000...

We prove combinatorial rules that give the minimal and maximal partitions labelling the irreducible constituents of a family of characters for the symmetric group that generalize Foulkes permutation characters. Restated in the language of symmetric functions, our results determine all minimal and maximal partitions that label Schur functions appearing in the plethysms sν ◦ s(m). As a corollary ...

LetG be a permutation group of degree n. The connection between themultiple transitivity of G and the irreducibility of certain irreducible characters of of the symmetric group Sn when restricted to G goes back to Frobenius, and a proof of his classical result can be found in Tsuzuku 1 . In 2 , Saxl strengthens this result, limiting the irreducibility hypothesis to the characters χ n−k,k G , a ...

We assume that the “table head” of the ordinary character table of the sporadic simple Janko group J4 is known. That is, the conjugacy classes and their centralizer orders are known as well as all p-th power maps, for primes p up to the maximal element order in J4, which is 66. For the sake of simplicity, we take the table head of the character table contained in the GAP Character Table Library...

We give a simple combinatorial proof of Ram’s rule for computing the characters of the Hecke Algebra. We also establish a relationship between the characters of the Hecke algebra and the Kronecker product of two irreducible representations of the Symmetric Group which allows us to give new combinatorial interpretations to the Kronecker product of two Schur functions evaluated at a Schur functio...