Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

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 Lu...

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Λεπτομέρειες βιβλιογραφικής εγγραφής
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:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Letellier, Emmanuel.  |e author. 
245 1 0 |a Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras  |h [electronic resource] /  |c by Emmanuel Letellier. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2005. 
300 |a XI, 165 p.  |b online resource. 
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490 1 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1859 
505 0 |a Preface -- Introduction -- Connected Reductive Groups and their Lie Algebras -- Deligne-Lusztig Induction -- Local Systems and Perverse Shaeves -- Geometrical Induction -- Deligne-Lusztig Induction and Fourier Transforms -- Fourier Transforms of the Characteristic Functions of the Adjoint Orbits -- References -- Index. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Group theory. 
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650 2 4 |a Group Theory and Generalizations. 
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776 0 8 |i Printed edition:  |z 9783540240204 
830 0 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1859 
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