The exotic Robinson-Schensted correspondence

TL;DR

This paper introduces an exotic version of the Robinson-Schensted correspondence derived from symplectic group actions on vector-flag pairs, linking geometric structures to representation theory.

Contribution

It develops a novel exotic Robinson-Schensted correspondence based on the symplectic group's action, extending classical combinatorial correspondences to new geometric contexts.

Findings

Identifies irreducible components of the conormal variety in this setting

Proposes a conjectural link between exotic cells and character sheaves

Establishes a new geometric framework for the correspondence

Abstract

We study the action of the symplectic group on pairs of a vector and a flag. Considering the irreducible components of the conormal variety, we obtain an exotic analogue of the Robinson-Schensted correspondence. Conjecturally, the resulting cells are related to exotic character sheaves.