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PreprintarXiv licencearXiv

Scary Wheels (and Super Shrubs)

  • Andrei Neguţ
  • Alexander Tsymbaliuk
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Abstract

We prove the shuffle realization for quantum affine superalgebras of types B,C,D in the loop realization, in that we construct an isomorphism between each of these algebras and a suitably defined double shuffle algebra. We explicitly describe the latter shuffle algebra using certain vanishing conditions that generalize the Feigin-Odesskii wheel conditions; a novel feature is the appearance of a so-called scary wheel, which is a particular order $2$ vanishing condition involving $7$ variables. Along the way, we fully develop the theory of shrubs in super types A (affine and toroidal), which are important combinatorial tools in the study of the shuffle algebras associated to toric Calabi-Yau threefolds. Our techniques also allow us to define quantum toroidal superalgebras of types B,C,D. More importantly, we provide a general framework to formulate and prove shuffle realizations in the wide generality of quivers with parameters.

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Cite

BibTeXRIS
BibTeX
@misc{neguţ2026scary,
  title = {{Scary Wheels (and Super Shrubs)}},
  author = {Andrei Neguţ and Alexander Tsymbaliuk},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00726},
  eprint = {2609.00726},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00726},
}
RIS
TY  - UNPB
TI  - Scary Wheels (and Super Shrubs)
AU  - Andrei Neguţ
AU  - Alexander Tsymbaliuk
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00726
UR  - https://arxiv.org/abs/2609.00726
AB  - We prove the shuffle realization for quantum affine superalgebras of types B,C,D in the loop realization, in that we construct an isomorphism between each of these algebras and a suitably defined double shuffle algebra. We explicitly describe the latter shuffle algebra using certain vanishing conditions that generalize the Feigin-Odesskii wheel conditions; a novel feature is the appearance of a so-called scary wheel, which is a particular order $2$ vanishing condition involving $7$ variables. Along the way, we fully develop the theory of shrubs in super types A (affine and toroidal), which are important combinatorial tools in the study of the shuffle algebras associated to toric Calabi-Yau threefolds. Our techniques also allow us to define quantum toroidal superalgebras of types B,C,D. More importantly, we provide a general framework to formulate and prove shuffle realizations in the wide generality of quivers with parameters.
ER  -