The space of invariant functions on a finite Lie algebra

Author:
G. I. Lehrer

Journal:
Trans. Amer. Math. Soc. **348** (1996), 31-50

MSC (1991):
Primary 20G40, 20G05; Secondary 22E60, 11T24

DOI:
https://doi.org/10.1090/S0002-9947-96-01492-4

MathSciNet review:
1322953

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Abstract: We show that the operations of Fourier transform and duality on the space of adjoint-invariant functions on a finite Lie algebra commute with each other. This result is applied to give formulae for the Fourier transform of a ``Brauer function''---i.e. one whose value at depends only on the semisimple part of and for the dual of the convolution of any function with the Steinberg function. Geometric applications include the evaluation of the characters of the Springer representations of Weyl groups and the study of the equivariant cohomology of local systems on , where is a maximal torus of the underlying reductive group .

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Additional Information

**G. I. Lehrer**

Affiliation:
address School of Mathematics and Statistics, University of Sydney, Sydney N.S.W. 2006, Australia

DOI:
https://doi.org/10.1090/S0002-9947-96-01492-4

Received by editor(s):
February 15, 1994

Article copyright:
© Copyright 1996
American Mathematical Society