UID:
almahu_9947363913602882
Format:
XI, 165 p.
,
online resource.
ISBN:
9783540315612
Series Statement:
Lecture Notes in Mathematics, 1859
Content:
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.
Note:
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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783540240204
Language:
English
URL:
http://dx.doi.org/10.1007/b104209
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