\(q\)-universal characters and an extension of the lattice \(q\)-universal characters. (English. Russian original) Zbl 1471.81116
Theor. Math. Phys. 208, No. 1, 896-911 (2021); translation from Teor. Mat. Fiz. 208, No. 1, 51-68 (2021).
Summary: We consider two different subjects: the \(q\)-deformed universal characters \(\widetilde S_{[\lambda,\mu]}(t,\hat t;x,\hat x)\) and the \(q\)-deformed universal character hierarchy. The former are an extension of \(q\)-deformed Schur polynomials, and the latter can be regarded as a generalization of the \(q\)-deformed KP hierarchy. We investigate solutions of the \(q\)-deformed universal character hierarchy and find that the solution can be expressed by the boson-fermion correspondence. We also study a two-component integrable system of \(q\)-difference equations satisfied by the two-component universal character.
MSC:
| 81V72 | Particle exchange symmetries in quantum theory (general) |
| 14D15 | Formal methods and deformations in algebraic geometry |
| 20C15 | Ordinary representations and characters |
| 20G43 | Schur and \(q\)-Schur algebras |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 39A13 | Difference equations, scaling (\(q\)-differences) |
Keywords:
\(q\)-deformation; universal character; \(q\)-deformed universal character hierarchy; boson-fermion correspondence; lattice \(q\)-deformed universal character hierarchyReferences:
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