Parabolic induction for Springer fibres

Lewis Topley, Neil Saunders

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Abstract

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.

Original languageEnglish
Pages (from-to)3331-3345
Number of pages15
JournalProceedings of the American Mathematical Society
Volume151
Issue number8
Early online date28 Apr 2023
DOIs
Publication statusPublished - 1 Aug 2023

Keywords

  • Springer fibres
  • Representation theory
  • Algebraic geometry

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