Matrix-Ball Construction of affine Robinson-Schensted correspondence
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 t...
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| Veröffentlicht in: | Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings, 28th... |
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| Hauptverfasser: | , , |
| Format: | Journal Article Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Schlagworte: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6396 |