Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian

Symmetry Integrability and Geometry-Methods and Applications

article

Takafumi Amaba¹  Roland Friedrich² 

[1] Fukuoka University;ETH Zürich, D-GESS

关键词: Loewner–Kufarev equation;    Grassmannian;    conformal field theory;    Witt algebra;    free probability theory;    Faber polynomial;    Grunsky coefficient;    signature 2020 Mathematics Subject Classification 35Q99;    30F10;    35C10;    58J65;   

DOI  :  10.3842/SIGMA.2020.108

来源: National Academy of Science of Ukraine

【 摘 要 】

We introduce the class of controlled Loewner-Kufarev equations and consider aspects of their algebraic nature. We lift the solution of such a controlled equation to the (Sato)-Segal-Wilson Grassmannian, and discuss its relation with the tau-function. We briefly highlight relations of the Grunsky matrix with integrable systems and conformal field theory. Our main result is the explicit formula which expresses the solution of the controlled equation in terms of the signature of the driving function through the action of words in generators of the Witt algebra.

【 授权许可】

Unknown