Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Authors: Liu, Si-Qi, Wang, Zhe, Zhang, Youjin
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211631
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals. Si-Qi Liu, Zhe Wang and Youjin Zhang. SIGMA 18 (2022), 037, 18 pages

We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge integrals in the way that one part of its flows yields the intermediate long wave hierarchy, and the remaining flows coin...