Lusztig $\mathbf{a}$-functions for quasiparabolic sets
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929632217923584 |
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| author | Zhang, Yifeng |
| author_facet | Zhang, Yifeng |
| contents | Kazhdan and Lusztig introduce the $W$-graphs to describe the cells and molecules corresponding to the Coxeter groups. Building on this foundation, Lusztig defines the a-funtion to classify the cells, as well as the molecules. Marberg then generalizes Kazhdan and Lusztig's $W$-graphs, using fixed-point-free involutions as their indices. The molecules of the two new $S_n$-graphs are then classified via two correspondence similar to RSK correspondence by Marberg and me. In this paper, we define an analogue of the Lusztig a-function and 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_2412_07810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lusztig $\mathbf{a}$-functions for quasiparabolic sets Zhang, Yifeng Combinatorics Representation Theory Kazhdan and Lusztig introduce the $W$-graphs to describe the cells and molecules corresponding to the Coxeter groups. Building on this foundation, Lusztig defines the a-funtion to classify the cells, as well as the molecules. Marberg then generalizes Kazhdan and Lusztig's $W$-graphs, using fixed-point-free involutions as their indices. The molecules of the two new $S_n$-graphs are then classified via two correspondence similar to RSK correspondence by Marberg and me. In this paper, we define an analogue of the Lusztig a-function and finish the classification of cells by proving that every molecule in the $S_n$-graphs is indeed a cell. |
| title | Lusztig $\mathbf{a}$-functions for quasiparabolic sets |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2412.07810 |