## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, J.-P. Bourguignon, M. Kotani, Y. Maeda and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 249 - 262

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

Masahiro Kasatani and Yoshihiro Takeyama

#### 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**

Received: 2 August 2007

First available in Project Euclid:
28 November 2018

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.2969/aspm/05510249

**Mathematical Reviews number (MathSciNet)**

MR2463501

**Zentralblatt MATH identifier**

1180.39011

**Subjects**

Primary: 39A13: Difference equations, scaling ($q$-differences) [See also 33Dxx] 33C52: Orthogonal polynomials and functions associated with root systems 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]

**Keywords**

qKZ equation affine Hecke algebra non-symmetric Macdonald polynomial

#### 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