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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 language | English |
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Pages (from-to) | 3331-3345 |

Number of pages | 15 |

Journal | Proceedings of the American Mathematical Society |

Volume | 151 |

Issue number | 8 |

Early online date | 28 Apr 2023 |

DOIs | |

Publication status | Published - 1 Aug 2023 |

## Keywords

- Springer fibres
- Representation theory
- Algebraic geometry

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Dive into the research topics of 'Parabolic induction for Springer fibres'. Together they form a unique fingerprint.## Projects

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