Related papers: Character values at elements of order 2

Order three elements in the exceptional groups of type G2 are classified up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is…

We find group cochains valued in currents giving explicit representatives for the $\text{GL}_2$-equivariant polylogarithm class of a torus. Based on the construction of weight-$2$ Eisenstein series for $\text{GL}_2$ from this polylogarithm…

We compute the character tables of the following groups with character theoretic methods, using known information about the conjugacy classes and about the character tables of some subgroups and factor groups: $Th$, $J_4$, $2.{}^2E_6(2)$,…

We classify blocks in the BGG category $\mathcal O$ of modules of non-integral weights for the exceptional Lie superalgebra $D(2|1;\zeta)$. We establish various reduction methods, which connect some types of non-integral blocks of…

We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a…

A general setting to study a certain type of formulas, expressing characters of the symmetric group $\mathfrak{S}_n$ explicitly in terms of descent sets of combinatorial objects, has been developed by two of the authors. This theory is…

Let $G$ be a finite group and $N<G$ a normal subgroup with $G/N$ abelian. We show how the conjugacy classes of $G$ in a given coset $qN$ relate to the irreducible characters of $G$ that are not identically $0$ on $qN$. We describe several…

We express the set of representations from a cyclic $p$-group to a connected $p$-compact group in terms of the associated reflection group and compute its cardinality for each exotic $p$-compact group.

Robinson showed that the character degrees are determined by knowing, for all $n$, the number of ways that the identity can be expressed as a product of $n$ commutators. Earlier, Strunkov showed that the existence of characters of…

A character of a finite group having degree $n$ takes values which may be expressed as sums of $n$ or fewer roots of unity. In this note, we prove a result which describes the irreducible constituents of generalized characters on abelian…

We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order $q$, and $t$ fixes pointwise an $n$-space.…

Ganter and Kapranov associated a 2-character to 2-representations of a finite group. Elgueta classified 2-representations in the category of 2-vector spaces 2Vect_k in terms of cohomological data. We give an explicit formula for the…

Let $d$ be a positive integer. We study the proportion of irreducible characters of infinite families of irreducible Coxeter groups whose values evaluated on a fixed element $g$ are divisible by $d$. For Coxeter groups of types $A_n, B_n$…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of level is that the level of a character, provided it is not too…

We restrict the possibilities for the character degrees of $p$-groups $G$ satisfying $|G:G'| = p^2$. E.g. if $G$ is of maximal class and has an irreducible character of degree $> p$, then it has such a character of degree at most…

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of alternating groups.

We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least $2$ associated with representations whose kernel is a congruence…

This paper has two goals: to prove certain properties of character series of graded algebras on which a finite group acts as algebra automorphisms and to provide a detailed analysis of representations of 5-dimensional Sklyanin algebras at…

Let $G$ be a finite group. Harada's conjecture II states that the ratio of the product of all the number of elements in conjugacy classes over that of all degrees of irreducible complex characters of $G$ is an integer. The ratio is called…