论文标题
明确实现$ u_ {q}发电机复杂幂的代数（\ mathfrak {sl}（3））$
On explicit realization of algebra of complex powers of generators of $U_{q}(\mathfrak{sl}(3))$
论文作者
论文摘要
在本说明中，我们证明了一个不可或缺的身份，涉及量子组$ u_ {q}发电机的复杂功能（\ mathfrak {sl}（3））$被认为是某些正主序列表示的某些正算子。这种身份代表了lusztig在量子群的发电机之间的分裂力之间的关系之一的连续类似物，这在研究不可约解模块\ cite {lu 1}中起着重要作用。我们还给出了$ u_ {q}的任意功能的定义（\ mathfrak {sl}（3））$生成器，并为有关$ u_ {q}（\ mathfrak {s sl}（sl}（3））$ u_ u_ {q}的正主序列表示的一些已知结果提供了其他证明。
In this note we prove an integral identity involving complex powers of generators of quantum group $U_{q}(\mathfrak{sl}(3))$ considered as certain positive operators in the setting of positive principal series representations. This identity represents a continuous analog of one of the Lusztig's relations between divided powers of generators of quantum groups, which play an important role in the study of irreducible modules \cite{Lu 1}. We also give definitions of arbitrary functions of $U_{q}(\mathfrak{sl}(3))$ generators and give another proofs for some of the known results concerning positive principal series representations of $U_{q}(\mathfrak{sl}(3))$.
