Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

Walter Borho

ISBN 10: 1461289106 / ISBN 13: 9781461289104

Edité par Birkhäuser, Birkhäuser Okt 2011, 2011

A propos de cet article

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 148 pp. Englisch.

N° de réf. du vendeur 9781461289104

Détails bibliographiques

• Titre: Nilpotent Orbits, Primitive Ideals, and Characteristic Classes
• Éditeur: Birkhäuser, Birkhäuser Okt 2011
• Date de parution: 2011
• Langue: anglais
• ISBN à 10 chiffres: 1461289106
• ISBN à 13 chiffres: 9781461289104
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 9 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 9 millimètres de profondeur
• Poids: 236 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.