## 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 language | English (US) |
---|---|

Pages (from-to) | 335-346 |

Number of pages | 12 |

Journal | Discrete Mathematics and Theoretical Computer Science |

State | Published - 2016 |

Externally published | Yes |

Event | 28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada Duration: Jul 4 2016 → Jul 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