Abstract The ( q , Q ) -current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic q-Schur algebras. In this paper, we study the ( q , Q ) -current algebra U q ( sl n 〈 Q 〉 [ x ] ) associated with the special linear Lie algebra sl n . In particular, we classify finite dimensional simple U q ( sl n 〈 Q 〉 [ x ] ) -modules.

中文翻译：

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(q,Q)-流代数的有限维简单模

摘要 与一般线性李代数相关的( q , Q ) -流代数是第二作者在研究分圆q-Schur代数的表示论时提出的。在本文中，我们研究了与特殊线性李代数 sl n 相关的 ( q , Q ) -当前代数 U q ( sl n < Q > [ x ] )。特别地，我们对有限维简单 U q ( sl n < Q > [ x ] ) - 模块进行分类。