On the coadjoint orbits of the unitriangular group
type: Item
instance of: scholarly article
title: On the coadjoint orbits of the unitriangular group
zbMATH Open document ID: 0847.20040
author: Carlos A. M. André
published in: Journal of Algebra
publication date: 1996-06-03T00:00:00Z
review text: This paper is a continuation of another work of the author [J. Algebra 176, No. 3, 959-1000 (1995; Zbl 0837.20050)]. Let \(U_n(K)\) be the group of all \(n\times n\) unipotent upper triangular matrices with coefficients in an algebraically closed field \(K\). Let \(u_n(K)\) denote the Lie algebra of all \(n\times n\) nilpotent upper triangular matrices and let \(u_n(K)^*\) be the dual space of \(u_n(K)\). The group \(U_n(K)\) acts on \(u_n(K)^*\) via the coadjoint representation: \((x\cdot f)(a)=f(xax^{-1})\) for \(x\in U_n(K)\), \(f\in u_n(K)^*\), \(a\in u_n(K)\). Then \(u_n(K)^*\) decomposes as the disjoint union \(u_n(K)^*=\bigcup V_D(\varphi)\) of some of its (basic) subvarieties. The main goal of this paper is to describe a certain decomposition of a basic subvariety \(V_D(\varphi)\) into \(U_n(K)\)-invariant subvarieties.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 869795
zbMATH Keywords: basic subvarieties
zbMATH Keywords: unipotent upper triangular matrices
zbMATH Keywords: Lie algebras
zbMATH Keywords: nilpotent upper triangular matrices
zbMATH Keywords: coadjoint representations
zbMATH Keywords: decompositions
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
full work available at URL: jabr.1996.0084
OpenAlex ID: W2029325973
DOI: 10.1006/JABR.1996.0084
description: scientific article; zbMATH DE number 869795