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

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.