Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected (, )-Point Functions, and Double Hurwitz Numbers

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Authors: Wang, Zhiyuan, Yang, Chenglang
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212046
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected (, )-Point Functions, and Double Hurwitz Numbers. Zhiyuan Wang and Chenglang Yang. SIGMA 19 (2023), 085, 33 pages

We derive an explicit formula for the connected (, )-point functions associated with an arbitrary diagonal tau-function (⁺, ⁻) of the 2d Toda lattice hierarchy using fermionic computations and the boson-fermion correspondence. Then, for fixed ⁻, we compute the KP-affine coordinates of (⁺, ⁻). As app...