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arXiv · 2604.27475

Gromov-Hausdorff Convergence of Spectral Truncations for Quantum Groups

Xintao Peng·Qin Wang
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Abstract

We study the quantum Gromov-Hausdorff convergence of spectral truncations for compact quantum groups. Using a proper length function, we define a Dirac operator and the associated spectral truncations. This work extends the previous convergence results for tori (Leimbach-van Suijlekom) to a broad class of quantum groups, and provides Gromov-Hausdorff convergence result for spectral truncations on quantum groups, encompassing both compact and discrete quantum groups. Our results are applicable to $SU(N)$,$SO(N)$ and discrete quantum groups with rapid decay.

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Xintao Peng, Qin Wang. 2026-04-30. Gromov-Hausdorff Convergence of Spectral Truncations for Quantum Groups. https://arxiv.org/abs/2604.27475

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