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