Recursive structures of molecules and cells in Gelfand $S_n$-graphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913139962937344 |
|---|---|
| author | Dai, Zhiqiang Zhang, Yifeng |
| author_facet | Dai, Zhiqiang Zhang, Yifeng |
| contents | $W$-graphs, representing the multiplication action of the standard basis on the canonical basis in the Iwahori-Hecke algebra are introduced by Kazhdan and Lusztig. Marberg defined a generalized $W$-graph, the Gelfand W-graph, corresponding to the Hecke algebra modules instead of Hecke algebras. To classify the molecules and cells of the Gelfand $S_n$-graphs, in this paper, we introduce a recursive structure of $S_n$ and then discuss the action of the recursive structure on the molecules. Using this struction, we show that a specific molecule is indeed a cell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17844 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recursive structures of molecules and cells in Gelfand $S_n$-graphs Dai, Zhiqiang Zhang, Yifeng Combinatorics Representation Theory $W$-graphs, representing the multiplication action of the standard basis on the canonical basis in the Iwahori-Hecke algebra are introduced by Kazhdan and Lusztig. Marberg defined a generalized $W$-graph, the Gelfand W-graph, corresponding to the Hecke algebra modules instead of Hecke algebras. To classify the molecules and cells of the Gelfand $S_n$-graphs, in this paper, we introduce a recursive structure of $S_n$ and then discuss the action of the recursive structure on the molecules. Using this struction, we show that a specific molecule is indeed a cell. |
| title | Recursive structures of molecules and cells in Gelfand $S_n$-graphs |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2605.17844 |