Star and weak star irreducible fully commutative elements in Coxeter groups of affine types $\widetilde{B}$ and $\widetilde{D}$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911102241079296 |
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| author | Biagioli, Riccardo Costantini, Luca Sasso, Elisa |
| author_facet | Biagioli, Riccardo Costantini, Luca Sasso, Elisa |
| contents | The star operation, originally introduced by Kazhdan and Lusztig, was later specialized by Ernst to the so-called weak star reduction on the set of fully commutative elements of a Coxeter group. In this paper, we classify the star and weak star irreducible fully commutative elements in Coxeter groups of affine types $\widetilde{B}_{n+1}$ and $\widetilde{D}_{n+2}$. Focusing then on the case of type $\widetilde{D}_{n+2}$, we use the classification of star irreducible elements to provide a new proof of the faithfulness of a diagrammatic representation of the corresponding generalized Temperley-Lieb algebra, along with an explicit description of Lusztig's $\mathbf{a}$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Star and weak star irreducible fully commutative elements in Coxeter groups of affine types $\widetilde{B}$ and $\widetilde{D}$ Biagioli, Riccardo Costantini, Luca Sasso, Elisa Combinatorics Group Theory The star operation, originally introduced by Kazhdan and Lusztig, was later specialized by Ernst to the so-called weak star reduction on the set of fully commutative elements of a Coxeter group. In this paper, we classify the star and weak star irreducible fully commutative elements in Coxeter groups of affine types $\widetilde{B}_{n+1}$ and $\widetilde{D}_{n+2}$. Focusing then on the case of type $\widetilde{D}_{n+2}$, we use the classification of star irreducible elements to provide a new proof of the faithfulness of a diagrammatic representation of the corresponding generalized Temperley-Lieb algebra, along with an explicit description of Lusztig's $\mathbf{a}$-function. |
| title | Star and weak star irreducible fully commutative elements in Coxeter groups of affine types $\widetilde{B}$ and $\widetilde{D}$ |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2508.08388 |