Nilpotent Orbits, Primitive Ideals, and Characteristic Classes : A Geometric Perspective in Ring Theory

Walter Borho

ISBN 10: 0817634738 / ISBN 13: 9780817634735

Edité par Birkhäuser Boston, Birkhäuser Boston, 1989

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The 'vertices' of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.

N° de réf. du vendeur 9780817634735

Détails bibliographiques

• Titre: Nilpotent Orbits, Primitive Ideals, and Characteristic Classes : A Geometric Perspective in Ring Theory
• Éditeur: Birkhäuser Boston, Birkhäuser Boston
• Date de parution: 1989
• Langue: anglais
• ISBN à 10 chiffres: 0817634738
• ISBN à 13 chiffres: 9780817634735
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 13 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 13 millimètres de profondeur
• Poids: 395 grammes

A propos de ce titre

Synopsis

1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n, C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.