Polynomial solutions of the Knizhnik-Zamolodchikov equations and Schur-Weyl duality
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2006
- DOI:
- 10.48550/arXiv.math/0610383
- arXiv:
- arXiv:math/0610383
- Bibcode:
- 2006math.....10383F
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Quantum Algebra;
- 05E10;
- 33C70
- E-Print:
- 14 pages, reference added