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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.11588 |
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| _version_ | 1866909734459670528 |
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| author | Biagioli, Riccardo Fatabbi, Giuliana Sasso, Elisa |
| author_facet | Biagioli, Riccardo Fatabbi, Giuliana Sasso, Elisa |
| contents | Let $(W,S)$ be an affine Coxeter system of type $\widetilde{B}$ or $\widetilde{D}$ and ${\rm TL}(W)$ the corresponding generalized Temperley-Lieb algebra. In this paper we define an infinite dimensional associative algebra made of decorated diagrams that is isomorphic to ${\rm TL}(W)$. Moreover, we describe an explicit basis for such an algebra consisting of special decorated diagrams that we call admissible. Such basis is in bijective correspondence with the classical monomial basis of the generalized Temperley-Lieb algebra indexed by the fully commutative elements of $W$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11588 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Diagrammatic representations of Generalized Temperley-Lieb algebras of affine type $\widetilde{B}$ and $\widetilde{D}$ Biagioli, Riccardo Fatabbi, Giuliana Sasso, Elisa Representation Theory Combinatorics 05E10, 16G30 Let $(W,S)$ be an affine Coxeter system of type $\widetilde{B}$ or $\widetilde{D}$ and ${\rm TL}(W)$ the corresponding generalized Temperley-Lieb algebra. In this paper we define an infinite dimensional associative algebra made of decorated diagrams that is isomorphic to ${\rm TL}(W)$. Moreover, we describe an explicit basis for such an algebra consisting of special decorated diagrams that we call admissible. Such basis is in bijective correspondence with the classical monomial basis of the generalized Temperley-Lieb algebra indexed by the fully commutative elements of $W$. |
| title | Diagrammatic representations of Generalized Temperley-Lieb algebras of affine type $\widetilde{B}$ and $\widetilde{D}$ |
| topic | Representation Theory Combinatorics 05E10, 16G30 |
| url | https://arxiv.org/abs/2212.11588 |