Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Authors: Dubrovin, Boris, Valeri, Daniele, Yang, Di
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211827
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method. Boris Dubrovin, Daniele Valeri and Di Yang. SIGMA 18 (2022), 077, 32 pages

For each affine Kac-Moody algebra ⁽ʳ⁾ₙ of rank ℓ, = 1,2, or 3, and for every choice of a vertex ₘ, = 0, …, ℓ, of the corresponding Dynkin diagram, by using the matrix-resolvent method, we define a gauge-invariant tau-structure for the associated Drinfeld-Sokolov hierarchy and give explicit formula...