论文标题
KZ连接mod $ p $的不变子捆绑和$ \ hat {sl} _2 $ verma模块mod $ p $
An invariant subbundle of the KZ connection mod $p$ and reducibility of $\hat{sl}_2$ Verma modules mod $p$
论文作者
论文摘要
当它的多维超几何解决方案是一维积分时，我们考虑了$ \ mathbb c $的Kz微分方程。我们还考虑了有限字段$ \ mathbb f_p $上的相同的微分方程。我们研究了这些微分方程在$ \ Mathbb f_p $上的多项式解决方案的空间，该方程在V. Schechtman和作者先前的工作中构建。这些多项式解决方案的模块定义了关联的Kz连接模型$ p $的不变子集合。我们描述了该分支的代数方程式，并认为该方程对应于相关的$ \ hat {sl} _2 $ verma模块$ \ mathbb f_p $的最高权重向量。
We consider the KZ differential equations over $\mathbb C$ in the case, when its multidimensional hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $\mathbb F_p$. We study the space of polynomial solutions of these differential equations over $\mathbb F_p$, constructed in a previous work by V. Schechtman and the author. The module of these polynomial solutions defines an invariant subbundle of the associated KZ connection modulo $p$. We describe the algebraic equations for that subbundle and argue that the equations correspond to highest weight vectors of the associated $\hat{sl}_2$ Verma modules over the field $\mathbb F_p$.
