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.

中文翻译：

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$$q$$ - 通用字符和格子的扩展 $$q$$ - 通用字符

摘要

我们考虑两个不同的主题：\(q\)变形的通用字符\(\widetilde S_{[\lambda,\mu]}(t,\hat t;x,\hat x)\)和\(q \) -变形的通用字符层次结构。前者是\(q\)-变形Schur多项式的扩展，后者可以看作是\(q\)-变形KP层次结构的推广。我们研究了\(q\)变形的通用字符层次结构的解决方案，并发现该解决方案可以用玻色子-费米子对应表示。我们还研究了由二分量通用特征满足的\(q\) -差分方程的二分量可积系统。