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Pentagon Equation in Deformation Quantization of Character Varieties
Abstract
Deformation quantizations of the moduli space of framed flat bundles live naturally in the Drinfeld category. Such quantizations were constructed using the so-called quantum fusion by Li-Bland and Ševera. We give a complete characterization of the dependence of this quantization on combinatorial choices, and prove that these quantizations are all isomorphic, forming vertices of an explicitly constructed complete commuting graph of algebra isomorphism. To this end, we extend the Kontsevich integral methods of Le and Murakami from even associators to all associators. Finally, we also prove that bi-invariant Haar measures provide traces on these quantizations.
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BibTeX
@misc{pulmann2026pentagon,
title = {{Pentagon Equation in Deformation Quantization of Character Varieties}},
author = {Ján Pulmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35446},
eprint = {2610.35446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35446},
}
RIS
TY - UNPB
TI - Pentagon Equation in Deformation Quantization of Character Varieties
AU - Ján Pulmann
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35446
UR - https://arxiv.org/abs/2610.35446
AB - Deformation quantizations of the moduli space of framed flat bundles live naturally in the Drinfeld category. Such quantizations were constructed using the so-called quantum fusion by Li-Bland and Ševera. We give a complete characterization of the dependence of this quantization on combinatorial choices, and prove that these quantizations are all isomorphic, forming vertices of an explicitly constructed complete commuting graph of algebra isomorphism. To this end, we extend the Kontsevich integral methods of Le and Murakami from even associators to all associators. Finally, we also prove that bi-invariant Haar measures provide traces on these quantizations.
ER -