辫群在量子SL_2上的Lawrence-Krammer-Bigelow表示
The Lawrence-Krammer-Bigelow Representations of the Braid Groups via Quantum SL_2
摘要：
利用广义韦尔马模构造了n股辫群B_n在自由Z[q，q^-1，s，s ^-1]-模W_{n,l}上的表示.通过构造显式的整基和同构，在适当地确定Laurent多项式环的参数后，证明了B_n的W_{n,2}同构于B_n的忠实Lawrence Krammer Bigelow表示.我们还证明了B_n-表示W_{n,l}在分式域Q（q，s）上是不可约的.
英文摘要：
We construct representations of the braid groups B_n on n strands on free Z[q,q^-1,s,s^-1]-modules W_{n,l} using generic Verma modules for an integral version of quantum sl_2. We prove that the W_{n,2} are isomorphic to the faithful Lawrence Krammer Bigelow representations of B_n after appropriate identification of parameters of Laurent polynomial rings by constructing explicit integral bases and isomorphism. We also prove that the B_n-representations W_{n,l} are irreducible over the fractional field Q (q,s).
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