Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
Publication year: 2005
: 978-3-540-31561-2
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.
: Mathematics and Statistics, Deligne-Lusztig induction, Fourier transforms, Lie Algebras, Lie algebra, character-sheaves, trigonometric sums
