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＜電子ブック＞
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras / by Emmanuel Letellier
(Lecture Notes in Mathematics. ISSN:16179692 ; 1859)

版	1st ed. 2005.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	XI, 165 p : online resource
著者標目	*Letellier, Emmanuel author SpringerLink (Online service)
件　名	LCSH:Group theory FREE:Group Theory and Generalizations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b104209

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