Progress in Mathematics

Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

A Geometric Perspective in Ring Theory

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

Free Preview

Buy this book

eBook $64.99
price for USA in USD
  • ISBN 978-1-4612-4558-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-8176-3473-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $84.99
price for USA in USD
  • ISBN 978-1-4612-8910-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

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.

Reviews

"…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


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $64.99
price for USA in USD
  • ISBN 978-1-4612-4558-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-8176-3473-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $84.99
price for USA in USD
  • ISBN 978-1-4612-8910-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Loading...

Bibliographic Information

Bibliographic Information
Book Title
Nilpotent Orbits, Primitive Ideals, and Characteristic Classes
Book Subtitle
A Geometric Perspective in Ring Theory
Authors
Series Title
Progress in Mathematics
Series Volume
78
Copyright
1989
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston, Inc.
eBook ISBN
978-1-4612-4558-2
DOI
10.1007/978-1-4612-4558-2
Hardcover ISBN
978-0-8176-3473-5
Softcover ISBN
978-1-4612-8910-4
Series ISSN
0743-1643
Edition Number
1
Number of Pages
VIII, 134
Topics