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

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

2006-10-11

arxiv.org/abs/math/0610383v3

Int. Math. Res. Not. IMRN 2007, no. 15, Art. ID rnm046

Mathematics

Representation Theory

14 pages, reference added

Scientific paper

10.1093/imrn/rnm0046

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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