Minimal polynomials of elements of order \(p\) in irreducible representations of Chevalley groups over fields of characteristic \(p\)
type: Item
instance of: scholarly article
title: Minimal polynomials of elements of order \(p\) in irreducible representations of Chevalley groups over fields of characteristic \(p\)
zbMATH Open document ID: 0941.20049
published in: Siberian Advances in Mathematics
publication date: 2000-04-13T00:00:00Z
review text: Let \(K\) be an algebraically closed field of nonzero characteristic, let \(G\) be a semisimple algebraic group over \(K\), and let \(G_\mathbb{C}\) be the algebraic group of the same type over the field \(\mathbb{C}\) of complex numbers. The minimal polynomial has the form \((x-1)^k\) with some natural \(k\) for any unipotent element \(t\) and an irreducible representation \(\rho\) of the Chevalley group \(G\). So, it is defined by the number \(k=k_\rho(t)\). This number is constant on conjugacy classes. The author constructs a natural bijection \(f\) from the set of unipotent conjugacy classes of \(G\) onto the same classes of \(G_\mathbb{C}\) such that, for every unipotent conjugacy class \(c\), the equality \(k_\varphi(c)=\min\{p,k_{\varphi_\mathbb{C}}(f(c))\}\) holds.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1431906
zbMATH Keywords: minimal polynomials
zbMATH Keywords: representations
zbMATH Keywords: Chevalley groups
zbMATH Keywords: unipotent conjugacy classes
author: I. D. Suprunenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1431906