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Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers — arXiv:2610.11427

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.11427
License (as archived): CC0-1.0
Archived: 2026-10-09T06:29:15.836Z
SHA-256 of the archived text: 5df06c32061cd16a2682dc45ae7565c771390253d8ecd65be68e5af680566997
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How to cite

Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers — arXiv:2610.11427 — arXiv (en), https://arxiv.org/abs/2610.11427 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2ff2e533c42e (Metraipolis archive dc_2ff2e533c42e, sha256 5df06c32061cd16a2682dc45ae7565c771390253d8ecd65be68e5af680566997)

BibTeX

@misc{dc2ff2e533c42e,
  title = {Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers — arXiv:2610.11427},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.11427},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2ff2e533c42e; sha256 5df06c32061cd16a2682dc45ae7565c771390253d8ecd65be68e5af680566997},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.11427. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We construct quantum cluster structures on a family of quantized $K$-theoretic Coulomb branches and prove that the associated loop-graded Koszul-perverse hearts give monoidal categorifications of these algebras. For each $r\geq1$, the gauge group is the image of $GL_2\times(\mathbb{C}^*)^r$ in $GL((\mathbb{C}^2)^r)$, where $(g,z_1,\ldots,z_r)$ acts on the $a$th summand by $gz_a$. Each initial seed has $r+2$ mutable and $r$ invertible frozen variables. Over $\mathbb{Z}[v^{\pm1}]$, the quantum cluster algebra coincides with its upper quantum cluster algebra and is isomorphic to the Grothendieck ring of the corresponding heart. Every quantum cluster monomial is represented by a simple object, and every mutation is realized by a short exact sequence. The proof uses a quadratic refinement compatible with mutation and explicit mutation sequences that produce the dressed monopole generators. The principal quiver has the four-punctured-sphere mutation type for $r=4$ and is mutation-infinite for $r\geq5$.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Representation Theory (math.RT) ; Algebraic Geometry (math.AG); Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.11427 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:53:57.390Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).