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Irreducible components of exotic Springer fibres II: The Exotic Robinson-Schensted algorithm

Irreducible components of exotic Springer fibres II: The Exotic Robinson-Schensted algorithm

Nandakumar, Vinoth, Rosso, Daniele and Saunders, Neil (2021) Irreducible components of exotic Springer fibres II: The Exotic Robinson-Schensted algorithm. Pacific Journal of Mathematics, 310 (2). pp. 447-485. ISSN 0030-8730 (Print), 1945-5844 (Online) (doi:https://doi.org/10.2140/pjm.2021.310.447)

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Abstract

Kato's exotic nilpotent cone was introduced as a substitute for the ordinary nilpotent cone of type C with nicer properties. The geometric Robinson-Schensted correspondence is obtained by parametrizing the irreducible components of the Steinberg variety (the conormal variety for the action of a semisimple group on two copies of its flag variety) in two different ways. In type A the correspondence coincides with the classical Robinson-Schensted algorithm for the symmetric group. Here we give an explicit combinatorial description of the geometric bijection that we obtained in our previous paper by replacing the ordinary type C nilpotent cone with the exotic nilpotent cone in the setting of the geometric Robinson-Schensted correspondence. This "exotic Robinson-Schensted algorithm'' is a new algorithm which is interesting from a combinatorial perspective, and not a naive extension of the type A Robinson-Schensted bijection.

Item Type: Article
Uncontrolled Keywords: Springer Fibres, Robinson-Schensted Correspondence
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > School of Computing & Mathematical Sciences (CAM)
Last Modified: 11 May 2021 13:47
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
Selected for REF2021: None
URI: http://gala.gre.ac.uk/id/eprint/32282

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