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
The mirabolic Hecke algebra
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MIRABOLIC QUANTUM sl2$$ {\mathfrak{sl}}_2 $$
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For a reductive group $G$, Steinberg established a map from the Weyl group to the set of nilpotent $G$-orbits by using moment maps on double flag varieties. In particular, in the case of the generalExpand
Irreducible components of exotic Springer fibres
TLDR
The irreducible components of exotic Springer fibres are described, and it is proved that they are naturally in bijection with standard bitableaux, and deduce the existence of an exotic Robinson–Schensted bijection. Expand
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