arXiv subjects

Thilo Henrich

Publications and source records attributed to Thilo Henrich.

4 recordsLinked to original sources

arXiv2012

Vector bundles on plane cubic curves and the classical Yang-Baxter equation

In this article, we develop a geometric method to construct solutions of the classical Yang-Baxter equation, attaching to the Weierstrass family of plane cubic curves and a pair of coprime positive integers, a family of classical r-matrices. It turns out that all elliptic r-matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin's classification and prove that they are degenerations of the corresponding elliptic solutions.

math.AG↗

arXiv2011

Remarks on rational solutions of Yang-Baxter equations

In this article, we study unitary rational solutions of the associative Yang-Baxter equation with three spectral parameters. We explain how such solutions arise from the geometry of vector bundles on a cuspidal cubic curve. Moreover, we investigate how these solutions are related to the quantum and classical Yang-Baxter equations.

math-ph↗

arXiv2011

Mutation-classes of diagrams via infinite graphs

We give a complete description of the cluster-mutation classes of diagrams of Dynkin types \mathbb{A},\mathbb{B},\mathbb{D} and of affine Dynkin types \mathbb{B}^{(1)},\mathbb{C}^{(1)},\mathbb{D}^{(1)} via certain families of diagrams.

math.RT↗

arXiv2010

Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation

In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $τ$ from the upper half-plane and an invertible $n \times n$ matrix $B$ with complex coefficients one can attach a solution of AYBE with values in $Mat_{n \times n}(\CC) \otimes Mat_{n \times n}(\CC)$, depending holomorphically on $τ$ and $B$. Moreover, we compute some of these solutions explicitly.

math.AG↗