Polynomial Solutions of the Knizhnik-Zamolodchikov Equations and Schur-Weyl Duality
Polynomial Solutions of the Knizhnik-Zamolodchikov Equations and Schur-Weyl Duality
复制标题
Knizhnik-Zamolodchikov 方程和 Schur-Weyl 对偶的多项式解
DOI：
10.1093/imrn/rnm046
复制
发表时间：
2007
影响因子：
1
通讯作者：
Felder Giovanni
中科院分区：
文献类型：
--
作者：
Felder Giovanni
对于参数的整数值，给出了具有任意不可约对称群的KZ方程解的积分公式。相应的积分可以有效地计算为由给定杨图确定的若干迭代残数，并给出系数为整数的多项式。推导是基于Schur-Weyl对偶性和Matsuo对原su (n) KZ方程的结果。在相应同调群的交点对上，讨论了带参数的解空间与-的对偶性。
An integral formula for the solutions of Knizhnik–Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric groupSNis presented for integer values of the parameter. The corresponding integrals can be computed effectively as certain iterated residues determined by a given Young diagram and give polynomials with integer coefficients. The derivation is based on Schur–Weyl duality and the results of Matsuo on the originalSU(n) KZ equation. The duality between the spaces of solutions with parametersmand −mis discussed in relation with the intersection pairing in the corresponding homology groups.