Parabolic induction for Springer fibres

Neil Saunders, Lewis Topley

OAI: oai:purehost.bath.ac.uk:publications/c845bc9a-1d87-46ec-ae1a-f91f277779d8 • DOI: https://doi.org/10.1090/proc/16361

Let G be a reductive group satisfying the standard hypotheses, with Lie algebra g. For each nilpotent orbit O ₀ in a Levi subalgebra g ₀ 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 O ₀ 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 were classified by Spaltenstein using standard tableaux. Our main result 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.

Springer fibres Representation theory Algebraic geometry