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Parabolic induction for Springer fibres

Saunders, N. & Topley, L. (2023). Parabolic induction for Springer fibres. Proceedings of the American Mathematical Society, 151(8), pp. 3331-3345. doi: 10.1090/proc/16361


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:
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