Classic and mirabolic Robinson-Schensted-Knuth correspondence for partial flags

Abstract

In this paper we first 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. Then we use this result to generalize the mirabolic Robinson-Schensted-Knuth correspondence defined by Travkin, to the case of two partial flags and a line.

27 pages, slightly rewritten to combine two papers into one and clarify some sections

References in corpus (2)

• Orbit closures in the enhanced nilpotent cone
• Mirabolic Robinson-Schensted-Knuth correspondence

Cited by in corpus (5)

• Robinson-Schensted-Knuth correspondence in the representation theory of the general linear group over a non-archimedean local field
• A Robinson-Schensted Correspondence for Partial Permutations
• Enhanced adjoint action and their orbits for the general linear group
• q-Whittaker functions, finite fields, and Jordan forms
• Generalized orbital varieties for Mirkovic-Vybornov slices as affinizations of Mirkovic-Vilonen cycles