TY - JOUR

T1 - Matrix-Ball Construction of affine Robinson–Schensted correspondence

AU - Chmutov, Michael

AU - Pylyavskyy, Pavlo

AU - Yudovina, Elena

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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 (Formula presented.) where P and Q are tabloids and (Formula presented.) is a dominant weight. The weights (Formula presented.) 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.

AB - 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 (Formula presented.) where P and Q are tabloids and (Formula presented.) is a dominant weight. The weights (Formula presented.) 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.

KW - Affine Weyl group

KW - Kazhdan–Lusztig cells

KW - Matrix-Ball Construction

KW - Robinson–Schensted correspondence

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U2 - 10.1007/s00029-018-0402-6

DO - 10.1007/s00029-018-0402-6

M3 - Article

SP - 1

EP - 84

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

SN - 1022-1824

ER -