Polynomial solutions of the KnizhnikZamolodchikov equations and SchurWeyl duality
Abstract
An integral formula for the solutions of KnizhnikZamolodchikov (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 SchurWeyl 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 DOI:
 10.48550/arXiv.math/0610383
 arXiv:
 arXiv:math/0610383
 Bibcode:
 2006math.....10383F
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra;
 05E10;
 33C70
 EPrint:
 14 pages, reference added