## Advanced Studies in Pure Mathematics

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

#### 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.

#### Article information

Dates
First available in Project Euclid: 28 November 2018

https://projecteuclid.org/ euclid.aspm/1543447912

Digital Object Identifier
doi:10.2969/aspm/05510249

Mathematical Reviews number (MathSciNet)
MR2463501

Zentralblatt MATH identifier
1180.39011

#### Citation

Kasatani, Masahiro; Takeyama, Yoshihiro. The quantum Knizhnik–Zamolodchikov equation and non-symmetric Macdonald polynomials. Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, 249--262, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05510249. https://projecteuclid.org/euclid.aspm/1543447912