Lecture Notes in Mathematics

Letellier, Emmanuel

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.

Details

Published by: Springer

Publication Date: 2004-12-02

Format: Paperback

ISBN-13: 9783540240204

DOI: 10.1007/b104209

Dimensions: 235cm x155cm

Pages: 165