论文标题
部分可观测时空混沌系统的无模型预测
Crystal bases and canonical bases for quantum Borcherds-Bozec algebras
论文作者
论文摘要
令$ u_ {q}^{ - }（\ mathfrak g）$为量子borcherds-bozec algebra $ u_ = u_ {q}（\ mathfrak g）$和$ v（λ）$是不可约束的最高权重模块，$λ\ in P^{+} $。在本文中，我们研究了$ u_ {q}^{ - }（\ Mathfrak g）$和$ v（λ）$之间的结构，属性及其在水晶基碱基和规范基础之间的紧密连接。我们首先使用经过修改的喀什瓦拉操作员重建晶体基理论。在经历喀西瓦拉（Kashiwara）的大循环论点时，我们证明了几个重要的引理，这些引理在本文后来的发展中扮演着至关重要的角色。接下来，基于量子bocherds-bozec代数的规范基础理论，我们介绍了原始规范基础的概念，并证明原始规范基础与较低的全球基础相吻合。
Let $U_{q}^{-}(\mathfrak g)$ be the negative half of a quantum Borcherds-Bozec algebra $U_{q}(\mathfrak g)$ and $V(λ)$ be the irreducible highest weight module with $λ\in P^{+}$. In this paper, we investigate the structures, properties and their close connections between crystal bases and canonical bases of $U_{q}^{-}(\mathfrak g)$ and $V(λ)$. We first re-construct crystal basis theory with modified Kashiwara operators. While going through Kashiwara's grand-loop argument, we prove several important lemmas, which play crucial roles in the later developments of the paper. Next, based on the theory of canonical bases on quantum Bocherds-Bozec algebras, we introduce the notion of primitive canonical bases and prove that primitive canonical bases coincide with lower global bases.
