Lecture Notes in Mathematics

Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

Authors: Letellier, Emmanuel

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About this book

The study of Fourier transforms of invariant functions on finite reductive Lie algebras has been initiated by T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.

Table of contents (9 chapters)

  • 1. Introduction

    Letellier, Emmanuel

    Pages 1-4

  • 2. Connected Reductive Groups and Their Lie Algebras

    Letellier, Emmanuel

    Pages 5-31

  • 3. Deligne-Lusztig Induction

    Letellier, Emmanuel

    Pages 33-43

  • 4. Local Systems and Perverse Sheaves

    Letellier, Emmanuel

    Pages 45-60

  • 5. Geometrical Induction

    Letellier, Emmanuel

    Pages 61-113

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-31561-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-24020-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1859
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-31561-2
DOI
10.1007/b104209
Softcover ISBN
978-3-540-24020-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XI, 165
Topics