布尔代数循环子的对称链分解及其与循环晶体的关系
Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals
摘要：
证明了布尔代数与循环群的商具有对称链分解。这推广了格里格斯、基利安和萨维奇关于素数阶的早期工作，给出了任何阶、素数或合数的明确构造。组合地图指定如何进行向下对称链中示出的是一个自然的循环模拟的$\mathfrak{sl}_2$降低运营商在理论的晶体基地。
英文摘要：
The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order, giving an explicit construction for any order, prime or composite. The combinatorial map specifying how to proceed downward in a symmetric chain is shown to be a natural cyclic analogue of the $\mathfrak{sl}_2$ lowering operator in the theory of crystal bases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
