Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
Letellier, Emmanuel.
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras [electronic resource] / by Emmanuel Letellier. - XI, 165 p. online resource. - Lecture Notes in Mathematics, 1859 0075-8434 ; . - Lecture Notes in Mathematics, 1859 .
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.
9783540315612
10.1007/b104209 doi
Group theory.
Group Theory and Generalizations.
QA174-183
512.2
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras [electronic resource] / by Emmanuel Letellier. - XI, 165 p. online resource. - Lecture Notes in Mathematics, 1859 0075-8434 ; . - Lecture Notes in Mathematics, 1859 .
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.
9783540315612
10.1007/b104209 doi
Group theory.
Group Theory and Generalizations.
QA174-183
512.2