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

Kasatani, Masahiro; Takeyama, Yoshihiro

doi:10.2969/aspm/05510249

VOL. 55 | 2009 The quantum Knizhnik–Zamolodchikov equation and non-symmetric Macdonald polynomials

Masahiro Kasatani, Yoshihiro Takeyama

Editor(s) Jean-Pierre Bourguignon, Motoko Kotani, Yoshiaki Maeda, Nobuyuki Tose

Adv. Stud. Pure Math., 2009: 249-262 (2009) DOI: 10.2969/aspm/05510249

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.