Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

Download or read book Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras written by Emmanuel Letellier and published by Springer. This book was released on 2004-11-15 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.