This article is cited in 5 papers

$q$-Universal characters and an extension of the lattice $q$-universal characters

Yang Gao^a, Chuanzhong Li<sup>ab

a</sup> School of Mathematics and Statistics, Ningbo University, Ningbo, China
^b College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

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.

Keywords: $q$-deformation, universal character, $q$-deformed universal character hierarchy, boson–fermion correspondence, lattice $q$-deformed universal character hierarchy.

MSC: 37K05, 37K10, 35Q53

Received: 11.12.2020
Revised: 21.01.2021

DOI: 10.4213/tmf10028

 English version: Theoretical and Mathematical Physics, 2021, 208:1, 896–911

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