Michael Chmutov ; Pavlo Pylyavskyy ; Elena Yudovina - Matrix-Ball Construction of affine Robinson-Schensted correspondence

dmtcs:6396 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6396
Matrix-Ball Construction of affine Robinson-Schensted correspondenceArticle

Authors: Michael Chmutov 1; Pavlo Pylyavskyy 1; Elena Yudovina 1

  • 1 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.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • PostDoctoral Research Fellowship; Funder: National Science Foundation; Code: 1503119
  • CAREER: Algebraic Combinatorics and URE; Funder: National Science Foundation; Code: 1351590
  • RTG in Combinatorics; Funder: National Science Foundation; Code: 1148634

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