Vol. 310, No. 2, 2021

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

Vinoth Nandakumar, Daniele Rosso and Neil Saunders

Vol. 310 (2021), No. 2, 447–485
DOI: 10.2140/pjm.2021.310.447
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 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.

Keywords
Springer fibres, Steinberg variety, Robinson–Schensted correspondence
Mathematical Subject Classification 2010
Primary: 05E10
Secondary: 20C30
Milestones
Received: 16 January 2020
Revised: 14 October 2020
Accepted: 15 December 2020
Published: 8 March 2021
Authors
Vinoth Nandakumar
School of Mathematics and Statistics
University of Sydney
Sydney
Australia
Daniele Rosso
Department of Mathematics and Actuarial Science
Indiana University Northwest
Gary, IN
United States
Neil Saunders
School of Computing and Mathematical Sciences
University of Greenwich
London
United Kingdom