City Research Online

Abstract

Let G be a reductive group satisfying the standard hypotheses, with Lie algebra g. For each nilpotent orbit Oₒ in a Levi subalgebra gₒ 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 Oₒ to the Springer fibre over O, which induces an injection on the level of irreducible components. When G = GLN 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.

Publication Type:	Article
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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