| Autor: |
Max Glick, Michael Chmutov, Pavlo Pylyavskyy |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Journal of Combinatorial Algebra. 4:111-140 |
| ISSN: |
2415-6302 |
| Popis: |
Berenstein and Kirillov have studied the action of Bender-Knuth moves on semistandard tableaux. Losev has studied a cactus group action in Kazhdan-Lusztig theory; in type $A$ this action can also be identified in the work of Henriques and Kamnitzer. We establish the relationship between the two actions. We show that the Berenstein-Kirillov group is a quotient of the cactus group. We use this to derive previously unknown relations in the Berenstein-Kirillov group. We also determine precise implications between subsets of relations in the two groups, which yields a presentation for cactus groups in terms of Bender-Knuth generators. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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