Cell Classification of Gelfand $S_n$-Graphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917381095292928 |
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| author | Zhang, Yifeng |
| author_facet | Zhang, Yifeng |
| contents | Kazhdan and Lusztig introduced the $W$-graphs, which represent the multiplication action of the standard basis on the canonical bais in the Iwahori-Hecke algebra. In the Hecke algebra module, Marberg defined two generalied $W$-graphs, called the Gelfand $W$-graphs. The classification of the molecules of the type $A$ Gelfand $S_n$-graphs are determined by two RSK-like insertion algorithms. We finish the classification of cells by proving that every molecule in the $S_n$-graphs is indeed a cell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cell Classification of Gelfand $S_n$-Graphs Zhang, Yifeng Combinatorics Representation Theory Kazhdan and Lusztig introduced the $W$-graphs, which represent the multiplication action of the standard basis on the canonical bais in the Iwahori-Hecke algebra. In the Hecke algebra module, Marberg defined two generalied $W$-graphs, called the Gelfand $W$-graphs. The classification of the molecules of the type $A$ Gelfand $S_n$-graphs are determined by two RSK-like insertion algorithms. We finish the classification of cells by proving that every molecule in the $S_n$-graphs is indeed a cell. |
| title | Cell Classification of Gelfand $S_n$-Graphs |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2503.21215 |