The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, II

Quiver varieties and quantum Knizhnik--Zamolodchikov equation

We show how equivariant volumes of tensor product quiver varieties of type A are given by matrix elements of vertex operators of centrally extended doubles of Yangians, and how they satisfy in some cases the rational, level 1, quantum Knizhnik--Zamolodchikov equation.

The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, I

Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus $g$ are given. Sheaves of representations of affine Krichever-Novikov algebras over a dense open subset of the moduli space of Riemann surfaces (respectively of smooth, projective complex curves) with $N$ marked points are introduced. It is shown that the tangent space of the moduli space at an arbitrary moduli point is isomorphic to a certain subspace of the Krichever-Novikov vector field algebra given by the data of the moduli point. This subspace is complementary to the direct sum of th…

希金斯和齐齐内克-扎莫洛多奇基夫连接在亏格为零的情况下是项目等价的

The Hitchin and Knizhnik-Zamolodchikov connections are projectively equivalent in the genus zero case

本文研究了在亏格为零且至少有三个标记点的情况下，齐齐内克-扎莫洛多奇基夫连接与希金斯连接之间的项目等价性，通过构造和分析这两个连接的向量丛来证明其等价性。

The q-deformed Knizhnik-Zamolodchikov-Bernard heat equation

We introduce a q-deformation of the genus one sl_2 Knizhnik-Zamolodchikov-Bernard heat equation. We show that this equation for the dependence on the moduli of elliptic curves is compatible with the qKZB equations, which give the dependence on the marked points.

Lax equations and Knizhnik-Zamolodchikov connection

Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by Knizhnik-Zamolodchikov operators. This provides a prequantization of the Lax system. The representation operators of Poisson commuting Hamiltonians of the Lax system projectively commute. If Hamiltonians depend only on action variables then the corresponding operators commute.

Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$

In this article, we consider the connection problem of the KZ (Knizhnik-Zamolodchikov) equation on the moduli space $\cM_{0,5}$, and show that the connection matrices are expressed in terms of the Drinfel'd associator. As the compatibility condition on the connection problem, we have the pentagon relation for the Drinfeld associators. As an application of the connection problem, we derive the five term relation for dilogarithms.