Skip to main content
  • Book
  • © 2005

Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

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

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (9 chapters)

  1. Front Matter

    Pages I-XI
  2. 1. Introduction

    • Emmanuel Letellier
    Pages 1-4
  3. 3. Deligne-Lusztig Induction

    • Emmanuel Letellier
    Pages 33-43
  4. 4. Local Systems and Perverse Sheaves

    • Emmanuel Letellier
    Pages 45-60
  5. 5. Geometrical Induction

    • Emmanuel Letellier
    Pages 61-113
  6. 6. Deligne-Lusztig Induction and Fourier Transforms

    • Emmanuel Letellier
    Pages 115-149
  7. References

    • Emmanuel Letellier
    Pages 159-162
  8. Index

    • Emmanuel Letellier
    Pages 163-165
  9. Back Matter

    Pages 166-167

About this book

The Fourier transforms of invariant functions on finite reductive Lie algebras are due to 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

  • Book Title: Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

  • Authors: Emmanuel Letellier

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b104209

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2005

  • Softcover ISBN: 978-3-540-24020-4Published: 02 December 2004

  • eBook ISBN: 978-3-540-31561-2Published: 15 November 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 165

  • Topics: Group Theory and Generalizations

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions