论文标题
$ u_q（\ Mathfrak {sl}（n+1）的Shapovalov元素）
Shapovalov Elements For $U_q(\mathfrak{sl}(N+1))
论文作者
论文摘要
对于简单的谎言代数，Shapovalov元素在Verma模块中产生最高的重量向量。这些元素的通常结构对某个Weyl组元素的长度进行了诱导。如果$ \ mathfrak {g} = \ mathfrak {sl}（n+1）$在[MUS22A]中给出了Shapovalov元素的显式表达式。在这里，我们将参数调整为$ \ mathfrak {g} $的量化包络代数。
For a simple Lie algebra, Shapovalov elements give rise to highest weight vectors in Verma modules. The usual construction of these elements uses induction on the length of a certain Weyl group element. If $\mathfrak{g}= \mathfrak{sl}(N+1)$ explicit expressions for Shapovalov elements were given in [Mus22a]. Here we adapt the argument to the quantized enveloping algebra of $\mathfrak{g}$.
