The quantum Knizhnik-Zamolodchikov equation and non-symmetric Macdonald polynomials

2006/08/31 by M. Kasatani, Kasatani, M., Y. Takeyama +1
Mathematics · Physics and Astronomy · #33C52 #39A13 #81R50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math-ph #math.MP #math.QA #math.RT #msc:33C52 #msc:39A13 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0608773

17 pages, no figure; final version, we added the paper by Di Francesco and Zinn-Justin in references

arxiv created 2007/04/06 · arxiv updated 2009/12/01

Abstract

We construct special solutions of the quantum Knizhnik-Zamolodchikov equation on the tensor product of the vector representation of the quantum algebra of type A_N-1. They are constructed from non-symmetric Macdonald polynomials through the action of the affine Hecke algebra. As a special case the matrix element of the vertex operators of level one is reproduced.

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