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[工程科技]Lectures on the dynamical Yang-Baxter equations
0
0 Lectures on the dynamical Yang-Baxter
0
2
y equations
a
M Pavel Etingof and Olivier Schiffmann
8
1
1 Introduction
]
A
Q This paper arose from a minicourse given by the first author at MIT in the
. Spring of 1999, when the second author extended and improved his lecture
h notes of this minicourse. It contains a systematic and elementary introduction
t
a to a new area of the theory of quantum groups – the theory of the classical and
m quantum dynamical Yang-Baxter equations.
[ The quantum dynamical Yang-Baxter equation is a generalization of the
ordinary quantum Yang-Baxter equation. It first appeared in physical litera-
2 ture in the work of Gervais and Neveu [GN], and was first considered from a
v
4 mathematical viewpoint by Felder [F], who attached to every solution of this
6 equation a quantum group, and an interesting system of difference equations,
0 - the quantum Knizhnik-Zamolodchikov-Bernard (qKZB) equation. Felder also
8 considered the classical analogue of the quantum dynamical Yang-Baxter equa-
0 tion – the classical dynamical Yang-Baxter equation. Since then, this theory was
9
9 systematically developed in many papers, some of which are listed below. By
/ now, the theory of the classical and quantum dynamical Yang-Baxter equations
h and their solutions has many applications, in particular to integrable systems
t
a
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