# Mirabolic Robinson–Shensted–Knuth correspondence

@article{Travkin2008MirabolicRC, title={Mirabolic Robinson–Shensted–Knuth correspondence}, author={Roman Travkin}, journal={Selecta Mathematica}, year={2008}, volume={14}, pages={727-758} }

Abstract.The set of orbits of GL(V) in Fl(V) × Fl(V) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Magyar, Weyman, and Zelevinsky. We describe a mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a… Expand

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