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Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

A Geometric Perspective in Ring Theory

By: Walter Borho,J.-L. Brylinski,R. MacPherson

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Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

A Geometric Perspective in Ring Theory

By: Walter Borho,J.-L. Brylinski,R. MacPherson

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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Page Count

141

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461245583

ISBN 13

9781461245582

Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

A Geometric Perspective in Ring Theory

By: Walter Borho,J.-L. Brylinski,R. MacPherson

Write a review Read reviews Take a Quiz Solve Book Puzzle

Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

A Geometric Perspective in Ring Theory

By: Walter Borho,J.-L. Brylinski,R. MacPherson

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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

141

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461245583

ISBN 13

9781461245582