Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras: 1859 (Lecture Notes in Mathematics, 1859) - Softcover

Letellier, Emmanuel

Softcover

ISBN 10: 3540240209 ISBN 13: 9783540240204

Publisher: Springer, 2004

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2004
• Language: English
• ISBN 10: 3540240209
• ISBN 13: 9783540240204
• Binding: Paperback
• Number of pages: 176