论文标题
$（Q，\ Mathbf {Q}）$的有限尺寸简单模块 - 当前代数
Finite dimensional simple modules of $(q, \mathbf{Q})$-current algebras
论文作者
论文摘要
$（q，\ m马理{q}）$ - 与通用线性lie代数相关的当前代数是由第二作者引入了Cyclotomic $ q $ -schur代数的代表理论。在本文中，我们研究$（Q，\ MathBf {q}）$ - 当前代数$ u_q（\ Mathfrak {sl} _n^{\ Langle \ Langle \ Mathbf {q} \ rangle} [X] [X] [X]）$与特殊的线性Lieleal LieAl lieAlgebra $ \ Mathfrak相关联。特别是，我们对有限尺寸简单$ u_q（\ Mathfrak {sl} _n^{\ langle \ Mathbf {q} \ rangle} [x]）$ - 模块进行分类。
The $(q, \mathbf{Q})$-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 $(q, \mathbf{Q})$-current algebra $U_q(\mathfrak{sl}_n^{\langle \mathbf{Q} \rangle}[x])$ associated with the special linear Lie algebra $\mathfrak{sl}_n$. In particular, we classify finite dimensional simple $U_q(\mathfrak{sl}_n^{\langle \mathbf{Q} \rangle}[x])$-modules.
