对称分支通过Laurent现象代数
Symmetric Branching via Laurent Phenomenon Algebras
- Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在约化分支代数上构造Laurent现象结构，识别为上层Laurent现象代数，获得theta基并计算分支重数，证明突变不变性。
AI中文摘要：
我们在约化分支代数上构造了Laurent现象结构。对于$A_{2n-1}\downarrow C_{n}$（$n\ge 2$）以及例外包含$D_4\downarrow G_2$、$E_6\downarrow F_4$和$F_4\downarrow B_4$，我们将分支代数识别为具有多项式冻结系数的上层Laurent现象代数。射影表示的度分纤维范畴给出了一个共同构造。它还为$B_3 \downarrow G_2$和$G_2\downarrow A_2$提供了$A_1$型的簇种子。我们给出了统一充分条件，将特殊的Keel--Yu镜像代数识别为具有合适二项式种子的上层Laurent现象代数。所得的theta基同时适应于冻结边界赋值。对于$A_{2n-1}\downarrow C_{n}$（$2\le n\le5$）以及其他例外包含，我们获得了由显式有理多面体锥的格点参数化的齐次theta基，其权纤维计算每个分支重数。我们还证明了在UFD上LP模式的有限上界的突变不变性。
英文摘要：
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.
