Insertion algorithms for Type $\mathrm{B}$ and $\mathrm{D}$ Gelfand $W$-graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929201873944576 |
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| author | Zhang, Yifeng |
| author_facet | Zhang, Yifeng |
| contents | Like the RSK correspondence for symmetric groups, Garfinkle defined a domino correspondence for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups. Similar to the Knuth relations, Taskin and Pietraho give the plactic relations for the domino correspondence and Bonnafé use them to classify the cells for type $\mathrm{B}$ Coxeter groups. We give some further properties of the plactic relations and use these relations to describe the bidirected edges and the molecules of Gelfand $W$-graphs for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Insertion algorithms for Type $\mathrm{B}$ and $\mathrm{D}$ Gelfand $W$-graphs Zhang, Yifeng Representation Theory Combinatorics Like the RSK correspondence for symmetric groups, Garfinkle defined a domino correspondence for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups. Similar to the Knuth relations, Taskin and Pietraho give the plactic relations for the domino correspondence and Bonnafé use them to classify the cells for type $\mathrm{B}$ Coxeter groups. We give some further properties of the plactic relations and use these relations to describe the bidirected edges and the molecules of Gelfand $W$-graphs for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups. |
| title | Insertion algorithms for Type $\mathrm{B}$ and $\mathrm{D}$ Gelfand $W$-graphs |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2312.14043 |