A. Zalesski

activity

20072026

most citedOn characters of Chevalley groups vanishing at the non-semisimple elements

3 citations · 6 across the 24 of their papers we have counts for

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17 papers · 1 filter

math.GR2026

Prime degree irreducible representations of simple algebraic groups and finite simple groups of Lie type

D. L. Flannery, A. E. Zalesski

Let $r, p$ be primes and $k$ be a positive integer. We show that if $G$ is a subgroup of $S L_{r} (p^{k})$ lying only in the non-geometric Aschbacher class $C_{9}$ , then $∣ G ∣$ is…

math.GR2023

Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups

Alexandre Zalesski

We study the irreducible representations of simple algebraic groups in which some non-central semisimple element has at most one eigenvalue of multiplicity greater than 1. We bound…

math.GR2022

Rational elements in representations of simple algebraic groups, I

Alexandre Zalesski

A finite order element $g$ of a group $G$ is called rational if $g$ is conjugate to $g^{i}$ for every integer $i$ coprime to the order $g$ . We determine all triples $(G, g, ϕ)$ , where…

math.GR2021

Representations of dimensions $(p^{n} \pm 1) /2$ of the symplectic group of degree $2 n$ over a field of characteristic $p$

Alexandre Zalesski, Irina Suprunenko

The irreducible representations $ϕ_{n}^{1}$ and $ϕ_{n}^{2}$ of the symplectic group $G_{n} = S p_{2 n} (P)$ over an algebraically closednfield $P$ of characteristic $p > 2$ with highest weights $ω_…

math.GR2020

Abelian subgroups and semisimple elements in $2$ -modular representations of the symplectic group $S p_{2 n} (2)$

Alexandre Zalesski

We determine the irreducible 2-modular representations of the symplectic group $G = S p_{2 n} (2)$ whose restriction to every abelian subgroup has a trivial constituent. A similar resul…

math.GR2018★ 2 cited

Almost cyclic elements in cross-characteristic representations of finite groups of Lie type

Lino Di Martino, Marco A. Pellegrini, Alexandre E. Zalesski

This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed fi…

math.GR2017

Invariants of maximal tori and unipotent constituents of some quasi-projective characters for finite classical groups

Alexandre Zalesski

We study the decomposition of certain reducible characters of classical groups as the sum of irreducible ones. Let $G$ be an algebraic group of classical type with defini…

math.GR2017

On p-stability in groups and fusion systems

László Héthelyi, Magdolna Szőke, Alexandre Zalesski

The aim of this paper is to generalise the notion of p-stability to fusion systems. We study the question how Qd(p) is involved in finite simple groups. We show that with a single…

math.GR2016

Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with single non-trivial Jordan block

Alexandre Zalesski, Donna Testerman

In this paper we prove the following result. Let $G$ be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field $F$ of character…

math.GR2016

Almost cyclic elements in Weil representations of finite classical groups

L. Di Martino, A. E. Zalesski

This paper is a significant part of a general project aimed to classify all irreducible representations of finite quasi-simple groups over an algebraically closed field, in which t…

math.GR2014

Irreducible characters of finite simple groups constant at the p-singular elements

M. A. Pellegrini, A. Zalesski

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 vanis…

math.GR2014★ 1 cited

Subgroups of simple algebraic groups containing regular tori, and irreducible representations with multiplicity 1 non-zero weights

Donna Testerman, Alexandre Zalesski

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple algebraic groups containing a regular torus. We call a torus regular if…

math.GR2013

On the Steinberg character of an orthogonal group over a finite field

A. E. Zalesski

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension

math.GR2013★ 3 cited

On characters of Chevalley groups vanishing at the non-semisimple elements

M. A. Pellegrini, A. E. Zalesski

Let G be a finite simple group of Lie type. In this paper we study characters of G that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal un…

math.GR2013

A uniform upper bound for the character degree sums and Gelfand-Graev-like characters for finite simple groups

Pablo Spiga, Alexandre Zalesski

Let G be a finite non-abelian simple group and let p be a prime. We classify all pairs (G,p) such that the sum of the complex irreducible character degrees of G is greater than the…

math.GR2012

Low dimensional projective indecomposable modules for Chevalley groups in defining characteristic

Alexandre E. Zalesski

The paper studies lower bounds for the dimensions of projective indecomposable modules for Chevalley groups G in defining characteristic p. The main result extending earlier one by…

math.GR2007

Large dimensional classical groups and linear spaces

Alan R. Camina, Nick Gill, A. E. Zalesski

Suppose that a group $G$ has socle $L$ a simple large-rank classical group. Suppose furthermore that $G$ acts transitively on the set of lines of a linear space $S$ . We p…

Prime degree irreducible representations of simple algebraic groups and finite simple groups of Lie type

Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups

Rational elements in representations of simple algebraic groups, I

Representations of dimensions (pn±1)/2 of the symplectic group of degree 2n over a field of characteristic p

Abelian subgroups and semisimple elements in 2-modular representations of the symplectic group Sp2n​(2)

Almost cyclic elements in cross-characteristic representations of finite groups of Lie type

Invariants of maximal tori and unipotent constituents of some quasi-projective characters for finite classical groups

On p-stability in groups and fusion systems

Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with single non-trivial Jordan block

Almost cyclic elements in Weil representations of finite classical groups

Irreducible characters of finite simple groups constant at the p-singular elements

Subgroups of simple algebraic groups containing regular tori, and irreducible representations with multiplicity 1 non-zero weights

On the Steinberg character of an orthogonal group over a finite field

On characters of Chevalley groups vanishing at the non-semisimple elements

A uniform upper bound for the character degree sums and Gelfand-Graev-like characters for finite simple groups

Low dimensional projective indecomposable modules for Chevalley groups in defining characteristic

Large dimensional classical groups and linear spaces

Representations of dimensions $(p^{n} \pm 1) /2$ of the symplectic group of degree $2 n$ over a field of characteristic $p$

Abelian subgroups and semisimple elements in $2$ -modular representations of the symplectic group $S p_{2 n} (2)$