论文标题
$ sl_2 $ qkz方程的解决方案modulo an Integer
Solutions of the $sl_2$ qKZ equations modulo an integer
论文作者
论文摘要
我们研究了QKZ差异方程式，其值在$ n $ -th张量的功率中$ sl_2 $表示$ v $，变量$ z_1，\ dots，z_n $和Integer步骤$κ$。对于任何与步骤$κ$相对高的整数$ n $，我们在变量中构建了一个多项式$ f_r（z）$ $ z_1，\ dots，z_n $，值$ v^{\ otimimes n} $中的值与这些coortination coortination coortination coortinate $ v^^$ v^”系数。我们表明，多项式$ f_r（z）$满足qkz方程模型$ n $。 多项式$ f_r（z）$是以多维Barnes积分形式给出的\ qkz/方程的超几何解决方案的类似物。
We study the qKZ difference equations with values in the $n$-th tensor power of the vector $sl_2$ representation $V$, variables $z_1,\dots,z_n$ and integer step $κ$. For any integer $N$ relatively prime to the step $κ$, we construct a family of polynomials $f_r(z)$ in variables $z_1,\dots,z_n$ with values in $V^{\otimes n}$ such that the coordinates of these polynomials with respect to the standard basis of $V^{\otimes n}$ are polynomials with integer coefficients. We show that the polynomials $f_r(z)$ satisfy the qKZ equations modulo $N$. Polynomials $f_r(z)$ are modulo $N$ analogs of the hypergeometric solutions of the \qKZ/ equations given in the form of multidimensional Barnes integrals.
