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Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
Paperback
Series: Lecture Notes in Mathematics, Book 1859
ISBN13: 9783540240204
Publisher: Springer Nature
Published: Dec 2 2004
Pages: 165
Weight: 0.60
Height: 0.40 Width: 6.10 Depth: 9.10
Language: English
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.
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