AI 中文总结
研究高度为二的阶梯平面划分提升作用的循环筛选结果，利用自旋晶体张量幂解释及电网络空间坐标环二次部分的灌木丛基证明，还探讨了所有度数上电典范基存在时对所有高度阶梯平面划分提升的循环筛选意义。
AI 中文摘要
我们证明了提升作用于高度为二的阶梯平面划分的循环筛选结果。我们的证明有两个主要代数输入：根据Pappe - Pfannerer - Schilling - Simone最近研究的自旋晶体张量幂对该提升作用的解释，以及Gao - Lam - Xu最近引入的电网络空间坐标环二次部分的灌木丛基。此外，我们解释了所有度数上电典范基的存在如何产生所有高度阶梯平面划分提升的循环筛选。
英文摘要
We prove a cyclic sieving result for the action of promotion on the staircase plane partitions of height two. Our proof has two major algebraic inputs: an interpretation of this promotion action in terms of tensor powers of the spin crystal that was recently studied by Pappe--Pfannerer--Schilling--Simone, and the bush basis of the degree two part of the coordinate ring of the space of electrical networks that was recently introduced by Gao--Lam--Xu. Moreover, we explain how the existence of an electrical canonical basis in all degrees would yield cyclic sieving for promotion of staircase plane partitions of all heights.
Comments23 pages, 8 figures
