Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group
Quantum Algebra
2025-12-29 v1 Operator Algebras
Abstract
We construct the first examples of purely continuous, -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 . Our techniques are based on quantum cluster theory, in particular as developed through the work of Fock and Goncharov.
Keywords
Cite
@article{arxiv.2512.21579,
title = {Quantum $SL^+(N,\mathbb{R})$ as a locally compact quantum group},
author = {K. De Commer and G. Schrader and A. Shapiro and C. Voigt},
journal= {arXiv preprint arXiv:2512.21579},
year = {2025}
}
Comments
112 pages, 21 figures