Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

• Κύριος συγγραφέας: Letellier, Emmanuel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
• Σειρά: Lecture Notes in Mathematics, 1859
• Θέματα: Mathematics.; Group theory.; Group Theory and Generalizations.
• Φυσική περιγραφή: XI, 165 p. online resource.
• ISBN: 9783540315612
• ISSN: 0075-8434 ;

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.