拟线性代数与可积性（海森堡图）

Braided Drinfeld and Heisenberg Doubles

In this paper, the Drinfeld center of a monoidal category is generalized to a class of mixed Drinfeld centers. This gives a unified picture for the Drinfeld center and a natural Heisenberg analogue. Further, there is an action of the former on the latter. This picture is translated to a description in terms of Yetter-Drinfeld and Hopf modules over quasi-bialgebras in a braided monoidal category. Via braided reconstruction theory, intrinsic definitions of braided Drinfeld and Heisenberg doubles are obtained, together with a generalization of the result in [Lu94] that the Heisenberg double is a …

Heisenberg模型的精确n-自旋动力学结构因子

Exact n-spinon dynamic structure factor of the Heisenberg model

利用自旋子图像，我们导出了自旋为1/2的海森堡模型的n-自旋子动力学结构因子的积分表示。

Bergman空间，共形平坦二维盘操作符和仿射Heisenberg顶点代数

Bergman space, Conformally flat 2-disk operads and affine Heisenberg vertex algebra

本文研究了Bergman空间的对称代数作为共形平坦二维盘操作符的代数结构，并将其与仿射Heisenberg顶点代数联系起来。

Quasi-particles in the principal picture of $\widehat{\mathfrak{sl}}_{2}$ and Rogers-Ramanujan-type identities

In their seminal work J. Lepowsky and R. L. Wilson gave a vertex-operator theoretic interpretation of Gordon-Andrews-Bressoud's generalization of Rogers-Ramanujan combinatorial identities, by constructing bases of vacuum spaces for the principal Heisenberg subalgebra of standard $\widehat{\mathfrak{sl}}_{2}$-modules, parametrized with partitions satisfying certain difference 2 conditions. In this paper we define quasi-particles in the principal picture of $\widehat{\mathfrak{sl}}_{2}$ and construct quasi-particle monomial bases of standard $\widehat{\mathfrak{sl}}_{2}$-modules for which princi…

Gauge Theory and Integrability, I

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in many details, and present the arguments in a concrete and down-to-earth way. Many interesting effects, including the leading nontrivial contributions to the $R$-matrix, the operator product expansion of line operators, the framing anomaly, and the quantum deformation that leads from $\mathfrak{g}[[z]]$ to the Yangian, are computed explicitly via Feynman diagra…