Matrix-Ball Construction of affine Robinson-Schensted correspondence

Michael Chmutov (1) , Pavlo Pylyavskyy (1) , Elena Yudovina (1)

1 UMN-MATH - School of Mathematics

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 combi- natorial realization of Shi's algorithm. As a biproduct, we also give a way to realize the affine correspondence via the usual Robinson-Schensted bumping algorithm. Next, inspired by Honeywill, we extend the algorithm to a bijection between extended affine symmetric group and 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.

Domaines: Combinatoire [math.CO]

Michael Chmutov, Pavlo Pylyavskyy, Elena Yudovina. Matrix-Ball Construction of affine Robinson-Schensted correspondence. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6396⟩. ⟨hal-02173388⟩