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Rotation fixed points of undecorated braid varieties and fusion rings of affine Lie algebras

  • Yuma Mizuno
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Abstract

Let G be a simply connected semisimple algebraic group. On the (undecorated) braid variety associated with a power of a Coxeter element, there is a finite-order autoequivalence, called the Zamolodchikov transformation, induced by cyclic rotation of words. In this paper, we show that the coarse moduli space of the fixed-point stack of this autoequivalence is isomorphic to the spectrum of the fusion ring of the corresponding affine Lie algebra. The above results also extend to twisted Coxeter elements, and the fusion rings of all affine Lie algebras are obtained in this way.

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Cite

BibTeXRIS
BibTeX
@misc{mizuno2026rotation,
  title = {{Rotation fixed points of undecorated braid varieties and fusion rings of affine Lie algebras}},
  author = {Yuma Mizuno},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02034},
  eprint = {2610.02034},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02034},
}
RIS
TY  - UNPB
TI  - Rotation fixed points of undecorated braid varieties and fusion rings of affine Lie algebras
AU  - Yuma Mizuno
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.02034
UR  - https://arxiv.org/abs/2610.02034
AB  - Let G be a simply connected semisimple algebraic group. On the (undecorated) braid variety associated with a power of a Coxeter element, there is a finite-order autoequivalence, called the Zamolodchikov transformation, induced by cyclic rotation of words. In this paper, we show that the coarse moduli space of the fixed-point stack of this autoequivalence is isomorphic to the spectrum of the fusion ring of the corresponding affine Lie algebra. The above results also extend to twisted Coxeter elements, and the fusion rings of all affine Lie algebras are obtained in this way.
ER  -