On special pieces, the Springer correspondence, and unipotent characters

Details On special pieces, the Springer correspondence, and unipotent characters On special pieces, the Springer correspondence, and unipotent characters

2006-06-03

arxiv.org/abs/math/0606075v2

Mathematics

Representation Theory

23 pages, expanded version with main theorem strengthened, to appear in American Journal of Mathematics

Scientific paper

Let G be a reductive algebraic group over the algebraic closure of a finite field 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(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.

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