Matrix-ball construction of affine robinson-schensted correspondence

Michael Chmutov, Pavlo Pylyavskyy, Elena Yudovina

Research output: Contribution to journalConference articlepeer-review

Abstract

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 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.

Original languageEnglish (US)
Pages (from-to)335-346
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2016
Externally publishedYes
Event28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada
Duration: Jul 4 2016Jul 8 2016

Bibliographical note

Funding Information:
†partially supported by NSF grants DMS-1148634 and DMS-1503119 ‡partially supported by NSF grants DMS-1148634, DMS-1351590, and Sloan Fellowship

Keywords

  • Affine symmetric group
  • Kazhdan-Lusztig theory
  • Robinson-Schensted correspondence

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