Study of hyergeometric systems with resonant parameters

利用仿射环上的微分算子环理论，证明了a -超几何系统当且仅当其参数向量非共振时是不可约的。在证明过程中，我们确定了a -超几何系统的不可约商。给出了不可约a -超几何商的第一合模的有限生成系统的一种计算方法。特别地，如果由A生成的半群是简单且有分数的，则给出了显式的生成器系统。

We have proved that an A-hypergeometric system is irreducible if and only if its parameter vector is nonresonant, using the theory of the ring of differential operators on an affine toric variety. In the course of the proof, we have determined the irreducible quotients of an A-hypergeometric system.We have presented a way of computing a finite system of generators of the first syzygy module of an irreducible A-hypergeometric quotient. In particular, if the semigroup generated by A is simplicial and scored, then an explicit system of generators has been given.