Nilpotent Orbits, Primitive Ideals, and Characteristic Classes

1. Front Matter

   Pages i-vii

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2. Introduction

   • W. Borho, J-L. Brylinski, R. MacPherson

   Pages 1-9

3. A Description of Springer’s Weyl Group Representations in Terms of Characteristic Classes of Cone Bundles

   • W. Borho, J-L. Brylinski, R. MacPherson

   Pages 10-30

4. Generalities on equivariant K—theory

   • W. Borho, J-L. Brylinski, R. MacPherson

   Pages 31-44

5. Equivariant K—theory of torus actions and formal characters

   • W. Borho, J-L. Brylinski, R. MacPherson

   Pages 45-67

6. Equivariant characteristic classes of orbital cone bundles

   • W. Borho, J-L. Brylinski, R. MacPherson

   Pages 68-94

7. Characteristic Classes and Primitive Ideals

   • W. Borho, J-L. Brylinski, R. MacPherson

   Pages 95-123

8. Back Matter

   Pages 124-134

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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.

• Algebra
• Cohomology
• Group representation
• Irreducibility
• cls
• homomorphism
• ring theory

"…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

• BUGH - FB7, Wuppertal 1, Federal Republic of Germany

  W. Borho

• Department of Mathematics, Pennsylvania State University, University Park, USA

  J-L. Brylinski

• Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

  R. MacPherson

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