Robinson-Schensted-Knuth correspondence in the geometry of partial flag varieties

TL;DR

This paper extends the Robinson-Schensted-Knuth correspondence to partial flag varieties, linking flag positions with geometric components, building on prior work for complete flags.

Contribution

It generalizes the RSK correspondence to partial flags, connecting combinatorial data with geometric structures in flag varieties.

Findings

Established a new correspondence for partial flags

Connected combinatorial and geometric properties of flag varieties

Extended classical results to a broader setting

Abstract

In this paper we generalize to the case of partial flags a result proved both by Spaltenstein and by Steinberg that relates the relative position of two complete flags and the irreducible components of the flag variety in which they lie, using the Robinson-Schensted-Knuth correspondence.