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On special pieces, the Springer correspondence, and unipotent characters
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 130, Number 5, October 2008
- pp. 1399-1425
- 10.1353/ajm.0.0019
- Article
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Let $G$ be a connected reductive algebraic group over the algebraic closure of a finite field ${\Bbb F}_q$ of good characteristic. In this paper, we demonstrate a remarkable compatibility between the Springer correspondence for $G$ and the parametrization of unipotent characters of $G({\Bbb F}_q)$. In particular, we show that in a suitable sense, ``large'' portions of these two assignments in fact coincide. This extends earlier work of Lusztig on Springer representations within special pieces of the unipotent variety.