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Mathematics - Algebra | Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

Series: Lecture Notes in Mathematics, Vol. 1859

Letellier, Emmanuel

2005, XI, 165 p.

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  • About this book

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.

Content Level » Research

Keywords » Deligne-Lusztig induction - Fourier transforms - Lie Algebras - Lie algebra - character-sheaves - trigonometric sums

Related subjects » Algebra

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