Parabolic induction for Springer fibres

2021/12/18 by Topley, Lewis, Saunders, Neil
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.09923

Abstract

Let G be a reductive group satisfying the standard hypotheses, with Lie algebra \mathfrakg. For each nilpotent orbit O₀ in a Levi subalgebra \mathfrakg₀ we can consider the induced orbit O defined by Lusztig and Spaltenstein. We observe that there is a natural closed morphism of relative dimension zero from the Springer fibre over a point of O₀ to the Springer fibre over O, which induces an injection on the level of irreducible components. When G = GL_N the components of Springer fibres was classified by Spaltenstein using standard tableaux. Our main results explains how the Lusztig--Spaltenstein map of Springer fibres can be described combinatorially, using a new associative composition rule for standard tableaux which we call stacking.

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