Abstract
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.
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Funding
Chuanzhong Li is supported by the National Natural Science Foundation of China under Grant No. 12071237 and K. C. Wong Magna Fund in Ningbo University.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 208, pp. 51-68 https://doi.org/10.4213/tmf10028.
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Gao, Y., Li, C. \(q\)-Universal characters and an extension of the lattice \(q\)-universal characters. Theor Math Phys 208, 896–911 (2021). https://doi.org/10.1134/S0040577921070047
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DOI: https://doi.org/10.1134/S0040577921070047