BISPECTRAL AND (gl N, gl M) DUALITIES
BISPECTRAL AND (gl N, gl M) DUALITIES
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双谱和 (gl N, gl M) 对偶性
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Varchenko
中科院分区：
文献类型：
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作者：
E. Mukhin;V. Tarasov;A. Varchenko
令V = p ij (x)e 为维度N = N 1 +···+N n 的拟多项式空间。将 V 的正则化基本算子定义为多项式微分算子 D = N i=0 A N −i (x)∂ i x 消灭 V，并且其首项系数 A 0 是最小可能次数的多项式。我们构造一个拟多项式空间 U = q ab (u)e zau ，其正则化基本算子是微分算子 N i=0 u i A N −i (∂ u)。空间 U 是通过适当的积分变换从 V 构造的。我们的积分变换对应于 KP 层次有理解空间（无穷大消失）的双谱对合，参见 [W]。作为积分变换属性的推论，我们获得了与 (gl N , gl M) 对偶高丁模型相关的两个主函数的临界点之间以及相应的 Bethe 向量之间的对应关系。
Let V = p ij (x)e be a space of quasi-polynomials of dimension N = N 1 +· · ·+N n. Define the regularized fundamental operator of V as the polynomial differential operator D = N i=0 A N −i (x)∂ i x annihilating V and such that its leading coefficient A 0 is a polynomial of the minimal possible degree. We construct a space of quasi-polynomials U = q ab (u)e zau whose regularized fundamental operator is the differential operator N i=0 u i A N −i (∂ u). The space U is constructed from V by a suitable integral transform. Our integral transform corresponds to the bispectral involution on the space of rational solutions (vanishing at infinity) to the KP hierarchy, see [W]. As a corollary of the properties of the integral transform we obtain a correspondence between critical points of the two master functions associated with the (gl N , gl M) dual Gaudin models as well as between the corresponding Bethe vectors.