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On connection between associators and 6j-symbols

  • Elena Lanina
  • Artem Novokhatnii
  • Alexey Sleptsov
  • Radomir Stepanov
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Abstract

We propose a new formula relating the rationalized Drinfeld associators obtained from the Knizhnik--Zamolodchikov equation to the quantum 6j-symbols of the algebra 𝒰q(g): $ U_{q} = U \cdot Ξ¦^{KZ}_{\mathbb{Q}} $. We prove this relation in the case of the slN Lie algebra for the tensor cube of the fundamental and the first symmetric representation. We also check it perturbatively for the slN algebra for representations [2]βŠ— [1] βŠ— [1], [2]βŠ— [2] βŠ— [1], the non-trivial cases with multiplicities --- [2,1]βŠ— 3, [2,2]βŠ— 3, and in the case of the so5 Lie algebra for the tensor cube of the fundamental representation.

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Cite

BibTeXRIS
BibTeX
@misc{lanina2026connection,
  title = {{On connection between associators and 6j-symbols}},
  author = {Elena Lanina and Artem Novokhatnii and Alexey Sleptsov and Radomir Stepanov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08044},
  eprint = {2610.08044},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08044},
}
RIS
TY  - UNPB
TI  - On connection between associators and 6j-symbols
AU  - Elena Lanina
AU  - Artem Novokhatnii
AU  - Alexey Sleptsov
AU  - Radomir Stepanov
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.08044
UR  - https://arxiv.org/abs/2610.08044
AB  - We propose a new formula relating the rationalized Drinfeld associators obtained from the Knizhnik--Zamolodchikov equation to the quantum 6j-symbols of the algebra 𝒰_q(g): $ U_{q} = U \cdot Ξ¦^{KZ}_{\mathbb{Q}} $. We prove this relation in the case of the sl_N Lie algebra for the tensor cube of the fundamental and the first symmetric representation. We also check it perturbatively for the sl_N algebra for representations [2]βŠ— [1] βŠ— [1], [2]βŠ— [2] βŠ— [1], the non-trivial cases with multiplicities --- [2,1]^βŠ— 3, [2,2]^βŠ— 3, and in the case of the so_5 Lie algebra for the tensor cube of the fundamental representation.
ER  -