A note on fermionic flows of the \(N=(1|1)\) supersymmetric Toda lattice hierarchy. (English) Zbl 1062.37074
Summary: We extend the Sato equations of the \(N=(1|1)\) supersymmetric Toda lattice hierarchy by two new infinite series of fermionic flows and demonstrate that the algebra of the flows of the extended hierarchy is the Borel subalgebra of the \(N=(2|2)\) loop superalgebra.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K60 | Lattice dynamics; integrable lattice equations |
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
Keywords:
two-dimensional bosonic Toda lattice hierarchy; bosonic and fermionic lattice fields; symmetriesReferences:
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