  Kato's exotic nilpotent cone was introduced as a substitute for the ordinary
nilpotent cone of type C with cleaner 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 type A the bijection
coincides with the classical Robinson-Schensted algorithm for the symmetric
group. Here we give a combinatorial description of the bijection obtained by
using the exotic nilpotent cone instead of ordinary type C nilpotent cone in
the geometric Robinson-Schensted correspondence; we refer this as the "exotic
Robinson-Schensted bijection". This is interesting from a combinatorial
perspective, and not a naive extension of the type A Robinson-Schensted
bijection.
