Nilpotent Orbits, Primitive Ideals, and Characteristic Classes: A Geometric Perspective in Ring Theory: 78 (Progress in Mathematics) - Hardcover

Brylinski, J.-L.; MacPherson, R.; Borho, Walter

 
9780817634735: Nilpotent Orbits, Primitive Ideals, and Characteristic Classes: A Geometric Perspective in Ring Theory: 78 (Progress in Mathematics)
Hardcover
ISBN 10: 0817634738 ISBN 13: 9780817634735
Verlag: Birkhäuser, 1989

Inhaltsangabe

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.

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Críticas

"...Most of the results in this book are not new. Instead the aim has been to use geometric (in place of the more traditional algebraic) methods in the constructions and proofs. This sheds new lights on the close connection between the three topics. The book is not self-contained. It relies heavily on previous work by the authors as well as on many basic facts both from algebraic groups, topology and representation theory. However, the authors have taken great care to make the book readable to people without complete background in these theories..."

--Zentralblatt Math

Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser
Erscheinungsdatum
1989
Sprache
Englisch
ISBN 10 
0817634738
ISBN 13 
9780817634735
Einband
Tapa dura
Anzahl der Seiten
148
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

Weitere beliebte Ausgaben desselben Titels

9781461289104: Nilpotent Orbits, Primitive Ideals, and Characteristic Classes: A Geometric Perspective in Ring Theory: 78 (Progress in Mathematics)

Vorgestellte Ausgabe

ISBN 10:  1461289106 ISBN 13:  9781461289104
Verlag: Birkhäuser, 2011
Softcover