Matrix-Ball Construction of affine Robinson–Schensted correspondence

@article{Chmutov2020MatrixBallCO,
  title={Matrix-Ball Construction of affine Robinson–Schensted correspondence},
  author={Michael Chmutov and Pavlo Pylyavskyy and Elena Yudovina},
  journal={Selecta Mathematica},
  year={2020},
  volume={24},
  pages={667-750}
}
In his study of Kazhdan–Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson–Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combinatorial realization of Shi’s algorithm. As a byproduct, we also give a way to realize the affine correspondence via the usual Robinson–Schensted bumping algorithm. Next, inspired by Lusztig and Xi, we extend the algorithm to a bijection between the extended affine symmetric group… 

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