Related papers: Irreducible Characters for Algebraic Groups in Cha…

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…

The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…

We describe an algorithm, which - given the characters of tilting modules and assuming that Donkin's tilting conjecture is true - computes the characters of simple modules for an algebraic group in any characteristic.

We give a new formula for the values of an irreducible character of the symmetric group S_n indexed by a partition of rectangular shape. Some observations and a conjecture are given concerning a generalization to arbitrary shapes.

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

For an irreducible character $\chi$ of a finite group $G$, let $\mathrm{cod}(\chi):=|G: \ker(\chi)|/\chi(1)$ denote the codegree of $\chi$, and let $\mathrm{cod}(G)$ be the set of irreducible character codegrees of $G$. In this note, we…

We continue the study of character sheaves on a not necessarily connected reductive group. We prove orthogonality formulas for certain characteristic functions.

A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

Let $G$ be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to $3$. We construct a canonical correspondence between irreducible characters of degree coprime to $3$ of $G$ and those…

Iwahori-Hecke algebras for the infinite series of complex reflection groups $G(r,p,n)$ were constructed recently in the work of Ariki and Koike, Brou\'e and Malle, and Ariki. In this paper we give Murnaghan-Nakayama type formulas for…

A classical theorem on character degrees states that if a finite group has fewer than four character degrees, then the group is solvable. We prove a corresponding result on character values by showing that if a finite group has fewer than…

We describe an algorithm for computing Schur indices of irreducible characters of a finite group $G$, based on computations within $G$ and its subgroups and with their character tables. The algorithm has been implemented within \Magma\ and…

In this paper we study finite p-solvable groups having irreducible complex characters chi in Irr(G) which take roots of unity values on the p-singular elements of G.

Let $G$ be a finite group and $\mathrm{Irr}(G)$ the set of all irreducible complex characters of $G$. Define the codegree of $\chi \in \mathrm{Irr}(G)$ as $\mathrm{cod}(\chi):=\frac{|G:\mathrm{ker}(\chi) |}{\chi(1)}$ and denote by…

We re-express the quantum Calogero-Sutherland model for the Lie algebra $E_6$ and the particular value of the coupling constant $\kappa=1$ by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we…

We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…

In a recent paper, we defined twisted unitary $1$-groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary $1$-groups correspond to irreducible products of characters thereby…

We are interested in determining the bound of the average of the degrees of the irreducible characters whose degrees are not divisible by some prime $p$ that guarantees a finite group $G$ of odd order is $p$-nilpotent. We find a bound that…