TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
T2  - Lecture Notes in Mathematics,
SN  - 9783540315612
AV  - QA174-183 
U1  - 512.2 23
PY  - 2005///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Group theory
KW  - Group Theory and Generalizations
N1  - 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; ZDB-2-SMA; ZDB-2-LNM
N2  - 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 Lusztigs 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
UR  - http://dx.doi.org/10.1007/b104209
ER  -