Year: 2026
Type: preprint
Abstract: We construct Laurent phenomenon structures on reductive branching algebras. For $A_{2n-1}\downarrow C_{n}$, $n\ge 2$, and the exceptional inclusions $D_4\downarrow G_2$, $E_6\downarrow F_4$, and $F_4\downarrow B_4$, 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 $B_3 \downarrow G_2$ and $G_2\downarrow A_2$. 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 $A_{2n-1}\downarrow C_{n}$ with $2\le n\le5$ 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.
Source: arXiv (Cornell University)
Author: Fei, Jiarui
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214722090