Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers

@misc{liu2026categorified,
  title = {{Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers}},
  author = {Tianle Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11427},
  eprint = {2610.11427},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11427},
}

TY  - UNPB
TI  - Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers
AU  - Tianle Liu
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.11427
UR  - https://arxiv.org/abs/2610.11427
AB  - We study the quantized K-theoretic Coulomb branches of framed star-shaped quivers with central gauge dimension n≥2, r−1 one-dimensional outer gauge vertices, and a one-dimensional framing at the central vertex. For n=2 and arbitrary r≥1, and for every n≥2 with 1≤ r≤5, we prove that the loop-graded Koszul-perverse heart is a monoidal categorification of the associated quantum cluster algebra over ℤ[v^±1]. This quantum cluster algebra coincides with its upper quantum cluster algebra. For all n≥2 and r≥1, we construct an explicit initial seed and identify the associated upper quantum cluster algebra with the Grothendieck ring of this heart. Every mutation is realized by a short exact sequence, and every quantum cluster monomial is represented by a simple object.
ER  -