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arXiv · 2508.07857

Quantum Metric Structures on Iwahori-Hecke Algebras

Mario Klisse·Helena Perović
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Abstract

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.

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BibTeXRIS

Mario Klisse, Helena Perović. 2025-08-11. Quantum Metric Structures on Iwahori-Hecke Algebras. https://arxiv.org/abs/2508.07857

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