论文标题
量子群集突变和减少单词图
Quantum cluster mutations and reduced word graphs
论文作者
论文摘要
我们给出了代数证明参与分裂量子组积极代表的Coxeter移动的独立性，从而完成了原始结构的差距。为此，我们在量子群集代数的语言中提出了一个新的量化版本的lusztig的注射性引理，该量子群的语言是通过山雀的引理减少到涉及涉及coxeter移动序列的序列形成等级3循环的计算的证明。我们提供了山雀的引理的新的，建设性的证明，并通过普遍的laurent多项式使用某些群集代数技巧，提供了这些等级3周期下量子群集突变所需的明确计算。
We give an algebraic proof of the independence of Coxeter moves involved in the construction of positive representations of split-real quantum groups, thus completing a gap in the original construction. To do this, we propose a new quantized version of Lusztig's Injectivity Lemma in the language of quantum cluster algebra, the proof of which by Tits' Lemma reduces to calculations involving sequences of Coxeter moves forming rank 3 cycles. We give a new, constructive proof of Tits' Lemma, and provide the required explicit computation of the quantum cluster mutations under these rank 3 cycles using certain cluster algebraic tricks via universally Laurent polynomials.
