In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model for the Lie algebra E8 and coupling constant κ = 1 by using the fundamental irreducible characters of the algebra as dynamical independent variables. Then, we compute the second order characters of the algebra and some higher order characters.

In order to explore Representation Theory as a logical follow-up to group theory, I attempt to enumerate the irreducible representations of GL2(Fq). In order to do so, I first introduce the idea of a representation and provide a simple example. Next, I prove the existance of an irreducible decomposition for a given representation and introduce a useful result of characters. Finally, four types ...

In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of the Iwahori-Hecke algebras of types An−1, Bn, and Dn. Our method is a generalization of a derivation of the Murnaghan-Nakayama formula for the irreducible characters of the symmetric group given by Curtis Greene. Greene’s approach is to sum up the diagonal entries of the matrices of certain cycle ...

We show that a generalization of Stanley-Féray character formula for characters of symmetric groups holds true for skew Young diagrams. This generalization is very useful for dealing with asymptotic questions; for example we use it to show that balanced skew Young diagrams have the asymptotic property of approximate factorization of characters and therefore the fluctuations of a randomly select...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

Many different definitions have been given for semistandard odd and even orthogonal tableaux which enumerate the corresponding irreducible orthogonal characters. Weightpreserving bijections have been provided between some of these sets of tableaux (see [3], [8]). We give bijections between the (semistandard) odd orthogonal Koike-Terada tableaux and the odd orthogonal Sundaram-tableaux and betwe...

Assume G is a finite symplectic group Sp2n(q) over a finite field Fq of odd characteristic. We describe the action of the automorphism group Aut(G) on the set Irr(G) of ordinary irreducible characters of G. This description relies on the equivariance of Deligne–Lusztig induction with respect to automorphisms. We state a version of this equivariance which gives a precise way to compute the autom...