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Polynomial solutions of the Knizhnik-Zamolodchikov equations and Schur-Weyl duality

Giovanni Felder·Alexander P. Veselov
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Abstract

An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group S_N is 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 original SU(n) KZ equation. The duality between the spaces of solutions with parameters m and -m is discussed in relation with the intersection pairing in the corresponding homology groups.

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Giovanni Felder, Alexander P. Veselov. 2006-11-03. Polynomial solutions of the Knizhnik-Zamolodchikov equations and Schur-Weyl duality. https://doi.org/10.1093/imrn%2Frnm0046

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