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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 

Pages (fromto)  33313345 
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 
Bibliographical note
Funding Information:Received by the editors January 12, 2022, and, in revised form, October 27, 2022, and December 12, 2022. 2020 Mathematics Subject Classification. Primary 17B45; Secondary 14M15, 14N10. The first author benefited from the LMS Scheme 4, grant number 42037. The second author’s research was supported by UKRI grants MR/S032657/1, MR/S032657/2, and MR/S032657/3.
Publisher Copyright:
© 2023 American Mathematical Society.
Keywords
 Springer fibres
 Representation theory
 Algebraic geometry
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Geometric Representation Theory and Walgebras
Topley, L. (PI) & Villarreal, J. (Researcher)
2/06/21 → 31/01/25
Project: Research council