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arXiv · 2512.21579

Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group

K. De Commer·G. Schrader·A. Shapiro·C. Voigt
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Abstract

We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of higher rank split real Lie groups in type $A$. Our techniques are based on quantum cluster theory, in particular as developed through the work of Fock and Goncharov.

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K. De Commer, G. Schrader, A. Shapiro, C. Voigt. 2025-12-25. Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group. https://arxiv.org/abs/2512.21579

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