Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

  • Authors
  • Emmanuel Letellier

Part of the Lecture Notes in Mathematics book series (LNM, volume 1859)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Emmanuel Letellier
    Pages 1-4
  3. Emmanuel Letellier
    Pages 33-43
  4. Emmanuel Letellier
    Pages 45-60
  5. Emmanuel Letellier
    Pages 61-113
  6. Emmanuel Letellier
    Pages 115-149
  7. Emmanuel Letellier
    Pages 159-162
  8. Emmanuel Letellier
    Pages 163-165
  9. Back Matter
    Pages 166-167

About this book

Introduction

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.

Keywords

Deligne-Lusztig induction Fourier transforms Lie Algebras Lie algebra character-sheaves trigonometric sums

Bibliographic information

  • DOI https://doi.org/10.1007/b104209
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-24020-4
  • Online ISBN 978-3-540-31561-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book