On special pieces, the Springer correspondence, and unipotent characters

• Autores: Pramod N. Achar, Daniel S. Sage
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 5, 2008, págs. 1399-1425
• Idioma: inglés
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• Resumen

  • 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.