Convex orderings in affine root systems
type: Item
instance of: scholarly article
title: Convex orderings in affine root systems
zbMATH Open document ID: 0848.17017
author: Paolo Papi
published in: Journal of Algebra
publication date: 1995-06-14T00:00:00Z
review text: Let \(\Delta^0\) be a root system of a finite-dimensional complex simple Lie algebra \({\mathfrak g}^0\). Fix a positive system \(\Delta^0_+\) in \(\Delta^0\). The author [Proc. Am. Math. Soc. 120, 661-665 (1994; Zbl 0799.20037)] gave the definition of a compatible subset \(L\) of \(\Delta^0_+\) and proved that a subset \(L\) of \(\Delta^0_+\) is compatible if and only if \(L\) is associated to a unique element \(w\) in the Weyl group of \(\Delta^0\), moreover, the ordering on a totally ordered subset \(L \subseteq \Delta^0_+\) depends on the reduced expression of \(w\). In this paper, the definition of a compatible subset \(L\) of \(\Delta_+^{re}\) has been given where \(\Delta_+^{re}\) is the set of positive real roots of an affine Kac-Moody Lie algebra \({\mathfrak g}\), and it is proved that the results for \({\mathfrak g}\) are analogous to those for \({\mathfrak g}^0\).
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 763920
zbMATH Keywords: convex orderings
zbMATH Keywords: root system
zbMATH Keywords: Weyl group
zbMATH Keywords: compatible subset
zbMATH Keywords: affine Kac-Moody Lie algebra
reviewed by: Zhonghu Chen
MaRDI profile type: Publication
full work available at URL: jabr.1995.1062
OpenAlex ID: W4213307689
DOI: 10.1006/JABR.1995.1062
description: scientific article; zbMATH DE number 763920