Matrix-Ball Construction of affine Robinson–Schensted correspondence
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Michael Chmutov [1] ; Pavlo Pylyavskyy [1] ; Elena Yudovina [1]
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[1] University of Minnesota
University of Minnesota
City of Minneapolis, Estados Unidos
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 667-750
- Idioma: inglés
- DOI: 10.1007/s00029-018-0402-6
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Resumen
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 and collection of triples (P,Q,ρ) where P and Q are tabloids and ρ is a dominant weight. The weights ρ get a natural interpretation in terms of the Affine Matrix-Ball Construction. Finally, we prove that fibers of the inverse map possess a Weyl group symmetry, explaining the dominance condition on weights.
