ENGLISH

Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

By Emmanuel Letellier (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2005
ISBN
3540240209, 9783540240204
DOI
10.1007/b104209
ISSN
0075-8434
Open Library ID
OL9763072M
Language
english
Format
PDF
Filesize
1 MB (1185978 bytes)
Series
Lecture Notes in Mathematics 1859
Edition
1
Pages
165\171
Library
Kolxo3
Time added
2009-07-20 03:45:11
Group Theory and Generalizations

Description

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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