Modular generalized Springer correspondence I: the general linear group

  • Pramod N. Achar

    Louisiana State University, Baton Rouge, USA
  • Anthony Henderson

    University of Sydney, Australia
  • Daniel Juteau

    Université de Caen Basse-Normandie, Caen, France
  • Simon Riche

    Université Blaise Pascal, Aubière, France

Abstract

We define a generalized Springer correspondence for the group GL() over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse sheaves on the nilpotent cone of GL() satisfying the ‘recollement’ properties, and with subquotients equivalent to categories of representations of a product of symmetric groups.

Cite this article

Pramod N. Achar, Anthony Henderson, Daniel Juteau, Simon Riche, Modular generalized Springer correspondence I: the general linear group. J. Eur. Math. Soc. 18 (2016), no. 7, pp. 1405–1436

DOI 10.4171/JEMS/618