Quantum Metric Structures on Iwahori-Hecke Algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918122088300544 |
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| author | Klisse, Mario Perović, Helena |
| author_facet | Klisse, Mario Perović, Helena |
| contents | Iwahori-Hecke algebras are $q$-deformations of group algebras of Coxeter groups. In this article, we initiate a systematic study of quantum metric structures on Iwahori-Hecke algebras by establishing that, for finite rank right-angled Coxeter systems, the canonical filtrations of the corresponding Iwahori-Hecke algebras satisfy the Haagerup-type condition introduced by Ozawa and Rieffel if and only if the Coxeter diagram's complement contains no induced squares. As a consequence, these algebras naturally inherit compact quantum metric space structures in the sense of Rieffel. Additionally, we investigate continuity phenomena in this framework by demonstrating that, as the deformation parameter $q$ approaches $1$, the deformed Iwahori-Hecke algebras converge to the group algebra of the Coxeter group in Latrémolière's quantum Gromov-Hausdorff propinquity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Metric Structures on Iwahori-Hecke Algebras Klisse, Mario Perović, Helena Operator Algebras Metric Geometry Rings and Algebras 20C08, 46L87, 20F55, 20F65 Iwahori-Hecke algebras are $q$-deformations of group algebras of Coxeter groups. In this article, we initiate a systematic study of quantum metric structures on Iwahori-Hecke algebras by establishing that, for finite rank right-angled Coxeter systems, the canonical filtrations of the corresponding Iwahori-Hecke algebras satisfy the Haagerup-type condition introduced by Ozawa and Rieffel if and only if the Coxeter diagram's complement contains no induced squares. As a consequence, these algebras naturally inherit compact quantum metric space structures in the sense of Rieffel. Additionally, we investigate continuity phenomena in this framework by demonstrating that, as the deformation parameter $q$ approaches $1$, the deformed Iwahori-Hecke algebras converge to the group algebra of the Coxeter group in Latrémolière's quantum Gromov-Hausdorff propinquity. |
| title | Quantum Metric Structures on Iwahori-Hecke Algebras |
| topic | Operator Algebras Metric Geometry Rings and Algebras 20C08, 46L87, 20F55, 20F65 |
| url | https://arxiv.org/abs/2508.07857 |