Journal of the European Mathematical Society

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Volume 18, Issue 7, 2016, pp. 1405–1436
DOI: 10.4171/JEMS/618

Published online: 2016-05-20

Modular generalized Springer correspondence I: the general linear group

Pramod N. Achar[1], Anthony Henderson[2], Daniel Juteau[3] and Simon Riche[4]

(1) Louisiana State University, Baton Rouge, USA
(2) University of Sydney, Australia
(3) Université de Caen Basse-Normandie, Caen, France
(4) Université Blaise Pascal, Aubière, France

We define a generalized Springer correspondence for the group GL($n$) 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($n$) satisfying the ‘recollement’ properties, and with subquotients equivalent to categories of representations of a product of symmetric groups.

Keywords: Springer correspondence, nilpotent cone, nilpotent orbits, perverse sheaves, cuspidal pairs, recollement, Fourier transform, modular reduction

Achar Pramod, Henderson Anthony, Juteau Daniel, Riche Simon: Modular generalized Springer correspondence I: the general linear group. J. Eur. Math. Soc. 18 (2016), 1405-1436. doi: 10.4171/JEMS/618