Generalized Springer correspondence for symmetric spaces associated to orthogonal groups

2017/08/10 by Shoji, Toshiaki, Yang, Gao
#20G05 #20G40 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1708.03038

Abstract

Let G = GL_N over an algebraically closed field of odd characteristic, and θ an involutive automorphism on G such that H = (G^θ)⁰ is isomorphic to SO_N. Then G^ιθ = \ g ∈ G | θ(g) = g^-1 \ is regarded as a symmetric space G/G^θ. Let G^ιθ_uni be the set of unipotent elements in G^ιθ. H acts on G^ιθ_uni by the conjugation. As an analogue of the generalized Springer correspondence in the case of reductive groups, we establish in this paper the generalized Springer correspondence between H-orbits in G^ιθ_uni and irreducible representations of various symmetric groups.

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