nLab dressing action

The concept is introduced by Kyoto school (Date, Miwa, Jimbo) around 1980s

• M. A. Semenov-Tian-Shansky, Poisson groups and dressing transformations, Zap. Nauchn. Sem. LOMI, 150 (1986), 119–142 mathnet.ru; Poisson Lie groups, quantum duality principle, and the quantum double, in: Math. aspects of conformal and topological field theories and quantum groups (South Hadley, MA, 1992), 219–248, Contemp. Math. 175, AMS 1994; Classical $r$-matrices, Lax equations, Poisson Lie groups and dressing transformations, in: Field theory, quantum gravity and strings, II (Meudon/Paris, 1985/1986), 174–214, Lec. Notes in Phys. 280, Springer 1987, MR89g:58098
• А.Г. Рейман, М.А. Семёнов-Тян-Шанский, Интегрируемые системы. Теоретико-групповой подход, monograph (2003)