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Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

Letellier, Emmanuel

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Título:
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
Autor: Letellier, Emmanuel
Assuntos: Fourier transformations ; Group theory ; Group Theory and Generalizations ; Mathematics ; Mathematics and Statistics
Descrição: 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.
Títulos relacionados: Lecture Notes in Mathematics
Editor: Berlin, Heidelberg: Springer
Data de criação/publicação: 2004
Formato: 171
Idioma: Inglês

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