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Generalized Hirota equations and representation theory. I: The case of SL(2) and \(\text{SL}_q(2)\). (English) Zbl 0985.37510

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B81 Applications of Lie (super)algebras to physics, etc.
35Q51 Soliton equations
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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