循环群中的总正性II：Chevalley生成器
Total positivity in loop groups II: Chevalley generators
摘要：
这是第二次在一系列文件发展的理论总积极的循环组。本文研究Chevalley生成元的无穷乘积。我们表明，组合学的无限减少的话的理论基础，并发展的形式主义的无穷序列的辫子移动，称为辫子限制。我们将此与一个偏序，称为极限弱序，无限减少的话。Chevalley生成元生成的极限半群具有超限结构。我们证明了一种形式的唯一因式分解的元素，在效果上减少他们的研究无穷乘积的顺序结构的自然数。对于后者的无穷乘积，我们表明，总是有一个因式分解，它匹配一个无限Coxeter元素。我们采用的技术工具之一是一个完全积极的交换引理，似乎是独立的利益。这个结果表明交换引理（在考克斯特群的背景下）与某些不等式形式的完全正性兼容。
英文摘要：
This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop the formalism of infinite sequences of braid moves, called a braid limit. We relate this to a partial order, called the limit weak order, on infinite reduced words. The limit semigroup generated by Chevalley generators has a transfinite structure. We prove a form of unique factorization for its elements, in effect reducing their study to infinite products which have the order structure of the natural numbers. For the latter infinite products, we show that one always has a factorization which matches an infinite Coxeter element. One of the technical tools we employ is a totally positive exchange lemma which appears to be of independent interest. This result states that the exchange lemma (in the context of Coxeter groups) is compatible with total positivity in the form of certain inequalities.
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