Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 5 min ago
PreprintarXiv licencearXiv

Symmetric Branching via Laurent Phenomenon Algebras

  • Jiarui Fei
Open at sourcePDFDOICite

Abstract

We construct Laurent phenomenon structures on reductive branching algebras. For A2n−1↓ Cn, n≥ 2, and the exceptional inclusions D4↓ G2, E6↓ F4, and F4↓ B4, we identify the branching algebras with upper Laurent phenomenon algebras, keeping the frozen coefficients polynomial. Degree-fibred categories of projective presentations give a common construction. It also gives cluster seeds of type A1 for B3 ↓ G2 and G2↓ A2. We give uniform sufficient conditions identifying a specialized Keel--Yu mirror algebra with an upper Laurent phenomenon algebra admitting a suitable binomial seed. The resulting theta basis is simultaneously adapted to the frozen boundary valuations. For A2n−1↓ Cn with 2≤ n≤5 and for the other exceptional inclusions, we obtain homogeneous theta bases parametrized by lattice points of explicit rational polyhedral cones, whose weight fibres compute every branching multiplicity. We also prove mutation invariance of finite upper bounds for LP patterns over a UFD.

Related

  1. Positivity for graph Laurent phenomenon algebras
    Ross Glew
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Linear Laurent phenomenon algebras are of finite type
    Oliver Daisey
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Laurent Symmetric Functions
    Hugo Fernández, Elena Kleinwort, Tianze Li +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. On the Isotropy Groups of Locally Finite Derivations of Laurent Polynomial Algebras
    Anderson Porto, Marcelo Veloso
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Branching Gaps, Coexistence, and Boundary Influence for the Ising Model on Spherically Symmetric Trees
    Farrukh Mukhamedov, Otabek Khakimov
    arXivPreprintCC BY-NC-SA 4.0Full textDynamical systemsMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{fei2026symmetric,
  title = {{Symmetric Branching via Laurent Phenomenon Algebras}},
  author = {Jiarui Fei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32425},
  eprint = {2609.32425},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32425},
}
RIS
TY  - UNPB
TI  - Symmetric Branching via Laurent Phenomenon Algebras
AU  - Jiarui Fei
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32425
UR  - https://arxiv.org/abs/2609.32425
AB  - We construct Laurent phenomenon structures on reductive branching algebras. For A_2n−1↓ C_n, n≥ 2, and the exceptional inclusions D_4↓ G_2, E_6↓ F_4, and F_4↓ B_4, we identify the branching algebras with upper Laurent phenomenon algebras, keeping the frozen coefficients polynomial. Degree-fibred categories of projective presentations give a common construction. It also gives cluster seeds of type A_1 for B_3 ↓ G_2 and G_2↓ A_2. We give uniform sufficient conditions identifying a specialized Keel--Yu mirror algebra with an upper Laurent phenomenon algebra admitting a suitable binomial seed. The resulting theta basis is simultaneously adapted to the frozen boundary valuations. For A_2n−1↓ C_n with 2≤ n≤5 and for the other exceptional inclusions, we obtain homogeneous theta bases parametrized by lattice points of explicit rational polyhedral cones, whose weight fibres compute every branching multiplicity. We also prove mutation invariance of finite upper bounds for LP patterns over a UFD.
ER  -