Skew RSK and the switching on ballot tableau pairs
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866908639207358464 |
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| author | Azenhas, Olga |
| author_facet | Azenhas, Olga |
| contents | In arXiv:1808.06095 we have introduced the Knuth class of the word recording a sequence of locations for repeated internal insertion operations in the Sagan-Stanley skew RSK correspondence, with no prescribed external insertion of new cells, to be a preserver for the $P$-tableau. As a consequence the Benkart-Sottile-Stroomer switching involution on ballot tableau pairs allows a realization as a recursive internal insertion procedure. This amounts to explain the various presentations of Littlewood-Richardson (LR) commuters and their coincidence predicted by Pak and Vallejo with contributions by Danilov and Koshevoi. In particular, the aforesaid presentation provides internal insertion as an alternative to Schützenberger- Lusztig involution (or evacuation) to constructing the Gelfand-Tsetlin pair in the Henriques-Kamnitzer $\mathfrak{gl}_n$-crystal commuter. In addition, the coincidence of LR commuters solves the Lecouvey-Lenart conjecture, recently further developed by Kumar-Torres, on bijections between the Kwon and Sundaram branching models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_06095 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Skew RSK and the switching on ballot tableau pairs Azenhas, Olga Combinatorics 05E05, 05E10, 05E14, 17B37, 68Q17 In arXiv:1808.06095 we have introduced the Knuth class of the word recording a sequence of locations for repeated internal insertion operations in the Sagan-Stanley skew RSK correspondence, with no prescribed external insertion of new cells, to be a preserver for the $P$-tableau. As a consequence the Benkart-Sottile-Stroomer switching involution on ballot tableau pairs allows a realization as a recursive internal insertion procedure. This amounts to explain the various presentations of Littlewood-Richardson (LR) commuters and their coincidence predicted by Pak and Vallejo with contributions by Danilov and Koshevoi. In particular, the aforesaid presentation provides internal insertion as an alternative to Schützenberger- Lusztig involution (or evacuation) to constructing the Gelfand-Tsetlin pair in the Henriques-Kamnitzer $\mathfrak{gl}_n$-crystal commuter. In addition, the coincidence of LR commuters solves the Lecouvey-Lenart conjecture, recently further developed by Kumar-Torres, on bijections between the Kwon and Sundaram branching models. |
| title | Skew RSK and the switching on ballot tableau pairs |
| topic | Combinatorics 05E05, 05E10, 05E14, 17B37, 68Q17 |
| url | https://arxiv.org/abs/1808.06095 |