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PreprintarXiv licencearXiv

Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions

  • Christof Geiss
  • David Hernandez
  • Bernard Leclerc
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Abstract

We extend our previous results on cluster structures in the Grothendieck rings of categories 𝒪sh for shifted quantum affine algebras to the non-simply laced types. We also show that, for all types, the formal power series expressions of the cluster monomials in terms of classes of positive prefundamental representations can be regarded as limits of cluster expansions, thus establishing their positivity.

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Cite

BibTeXRIS
BibTeX
@misc{geiss2026representations,
  title = {{Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions}},
  author = {Christof Geiss and David Hernandez and Bernard Leclerc},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37184},
  eprint = {2610.37184},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37184},
}
RIS
TY  - UNPB
TI  - Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions
AU  - Christof Geiss
AU  - David Hernandez
AU  - Bernard Leclerc
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37184
UR  - https://arxiv.org/abs/2610.37184
AB  - We extend our previous results on cluster structures in the Grothendieck rings of categories 𝒪^sh for shifted quantum affine algebras to the non-simply laced types. We also show that, for all types, the formal power series expressions of the cluster monomials in terms of classes of positive prefundamental representations can be regarded as limits of cluster expansions, thus establishing their positivity.
ER  -