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Abstract
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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 parametrising 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.
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Keywords
Springer fibres, Steinberg variety, Robinson–Schensted
correspondence
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Mathematical Subject Classification 2010
Primary: 05E10
Secondary: 20C30
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Milestones
Received: 16 January 2020
Revised: 14 October 2020
Accepted: 15 December 2020
Published: 8 March 2021
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