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Transactions of the American Mathematical Society

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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 $X$ depends only on the semisimple part $X_s$ of $X$ 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 $G/T$, where $T$ is a maximal torus of the underlying reductive group $G$.


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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

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