论文标题
$ u_q \ mathfrak {sl}（2）$ verma-modules及其编织表示形式的同源模型
A homological model for $U_q \mathfrak{sl}(2)$ Verma-modules and their braid representations
论文作者
论文摘要
我们将劳伦斯对辫子组的表示将相对同源模块扩展到相对同源模块，并且我们表明它们是洛朗多项式环上的自由模块。我们定义同源运算符，并表明他们实际上为$ u_q \ mathfrak {sl}（2）$的积分版本提供了表示形式。我们建议在给定的同源模块的给定基础与Verma模块的张量产物的标准基础之间存在同构，并且我们表明它可以保留系数的积分环，即$ u_q \ mathfrak {sl}（2）$的作用，编织组表示及其分级。这为Kohno定理恢复了一个不可或缺的版本，该版本将绝对劳伦斯表示与最高权重向量上的量子编织表示。当我们摆脱参数的通用条件时，它是后者定理的扩展，并且当我们恢复Verma-Modules作为编织组的整个产品和$ U_Q \ Mathfrak {SL}（2）$ - 模块时。
We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. We define homological operators and we show that they actually provide a representation for an integral version for $U_q \mathfrak{sl}(2)$. We suggest an isomorphism between a given basis of homological modules and the standard basis of tensor products of Verma modules, and we show it to preserve the integral ring of coefficients, the action of $U_q \mathfrak{sl}(2)$, the braid group representations and their grading. This recovers an integral version for Kohno's theorem relating absolute Lawrence representations with quantum braid representation on highest weight vectors. It is an extension of the latter theorem as we get rid of generic conditions on parameters, and as we recover the entire product of Verma-modules as a braid group and a $U_q \mathfrak{sl}(2)$-module.
