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.
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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.
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cuspidal datum, geometrical induction, nilpotent pair, cuspidal pair, cuspidal data, perverse sheaf, admissible complexes, irreducible local system, following cartesian diagram, character sheaves, perverse sheaves, complex ind, intersection cohomology complex, complexes ind, constant attached, parabolic induction, algebra version, commutation formula, algebra decomposition, orbital pair, nilpotent orbits, parabolic subgroup, maximal torus, reductive groups, isomorphic classes Key Phrases - Capitalized Phrases (CAPs): (learn more)
F-stable Levi, Existence of Chevalley Bases, F-stable Borel New!
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cuspidal datum, geometrical induction, nilpotent pair, cuspidal pair, cuspidal data, perverse sheaf, admissible complexes, irreducible local system, following cartesian diagram, character sheaves, perverse sheaves, complex ind, intersection cohomology complex, complexes ind, constant attached, parabolic induction, algebra version, commutation formula, algebra decomposition, orbital pair, nilpotent orbits, parabolic subgroup, maximal torus, reductive groups, isomorphic classes Key Phrases - Capitalized Phrases (CAPs): (learn more)
F-stable Levi, Existence of Chevalley Bases, F-stable Borel New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 37
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- Geometric Curve Evolution and Image Processing (Lecture Notes in Mathematics) by Frédéric Cao in Back Matter
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- Heegner Modules and Elliptic Curves (Lecture Notes in Mathematics) by Martin L. Brown in Back Matter
- Noncommutative Geometry by Alain Connes in Back Matter
- Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction (Lecture Notes in Mathematics) by Dang D. Ang in Back Matter
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- Quantum Independent Increment Processes I: From Classical Probability to Quantum Stochastic Calculus (Lecture Notes in Mathematics) (v. 1) by David Applebaum in Back Matter
- Combinatorial Stochastic Processes: Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002 (Lecture Notes in Mathematics / École d'Été de Probabilités de Saint-Flour) (v. 32) by Jim Pitman in Back Matter
- Geometry of Müntz Spaces and Related Questions (Lecture Notes in Mathematics) by Vladimir I. Gurariy in Back Matter
- Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics) by Roger Mansuy in Back Matter
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