# Values of the Fourier transforms of Green functions at regular elements

## Author

**David G. A. Jackson**

## Status

Research Report 98-18

Date: 16 June 1998

To appear in Journal of Algebra

## Abstract

The complex characters of a finite reductive algebraic group G are largely
controlled by Green functions, which are the restrictions of certain
Deligne-Lusztig induced characters to unipotent elements of G. Treating
the Green functions as functions on Lie(G) supported on nilpotent elements,
Springer has shown that the Green functions can be expressed in terms of
the Fourier transforms of certain nilpotently supported Ad(G)-invariant
functions on Lie(G).
In this paper, we give a simple formula for the values of the Fourier
transforms of the Green functions at regular elements of Lie(G). The
computation uses the methods of intersection cohomology.

## Key phrases

reductive group. Green function. invariant function. coset induction.
Fourier transform. Lie algebra. intersection cohomology. perverse sheaf.

## AMS Subject Classification (1991)

Primary: 20G40

Secondary: 17B45, 55N33

## Content

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