Related papers: Vanishing-off subgroups and supercharacter theory …

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is…

The configuration of theta characteristics and vanishing thetanulls on a hyperelliptic curve is completely understood. We observe in this note that analogous results hold for the s-invariant theta characteristics on any curve C with an…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the…

We propose a definition of characters in the context of Schneider-Teitelbaum's theory of locally analytic representations of p-adic reductive groups. This character will be a function on a compact subgroup of a maximal torus of the…

We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups $\Gamma_1(N)$ and find the product identities which characterize super-replicable functions. These will provide a clue…

We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.

A new conjecture on characters of finite groups, related to the McKay conjecture, was proposed recently by the first and third authors. In this paper, we prove it for $p$-solvable groups when $p$ is odd.

In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the…

Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…

In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize…

We introduce a generalization of the product expansion of a finite semigroup. As an application, we provide an alternative proof of the decidability of pointlike sets for pseudovarieties consisting of semigroups whose subgroups all belong…

Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\theta$ be an irreducible character of $N$. We count the real irreducible characters of $G$ lying over $\theta$

In this paper we study irreducible tensor products of representations of alternating groups and classify such products in characteristic 5.

We call an irreducible character $p$-singular if $p$ divides its degree. We prove a number of equivalent conditions for a character of the symmetric group $S_n$ to be $p$-singular, involving a certain family of conjugacy classes. This…

This paper describes how to use subgroups to parameterize unipotent classes in the classical algebraic group in characteristic 2. These results can be viewed as an extension of the Bala-Carter Theorem, and give a convenient way to compare…

We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…

In this paper we introduce the notion of $\Delta$-weak character amenable Banach algebras and investigate $\Delta$-weak character amenability of certain Banach algebras such as projective tensor product $A\widehat{\otimes}B$, Lau product…

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These…

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…