论文标题
代数$ \ mathfrak {sp} _4 $和超几何功能的Gelfand-Tsetlin类型基础
A Gelfand-Tsetlin type base for the algebra $\mathfrak{sp}_4$ and hypergeometric functions
论文作者
论文摘要
在本文中，考虑了Lie代数$ \ Mathfrak {sp} _4 $在Lie Group $ SP_4 $上的功能空间中的表示。我们找到了与$ \ mathfrak {sp} _4 $ d.p.构建的$ \ mathfrak {sp} _4 $的gelfand-tsetlin类型向量相对应的函数。 Zhelobenko。此功能以$ $ a $ - 流行地几个地面功能表示。在开发了一些新技术之后，我们得出了分析公式，以实现该基础中代数的发电机的作用（以前尚不清楚）。这些公式比Molev构建的Gelfand-Tsetlin型基碱基中发电机的作用的公式要困难得多。
In the paper a realization of representation of a Lie algebra $\mathfrak{sp}_4$ in the space of function on the Lie group $Sp_4$ is considered. We find a function corresponding to a Gelfand-Tsetlin type vector for $\mathfrak{sp}_4$ constructed by D.P. Zhelobenko. This function is expressed though a $A$-hypergeometric function. After developing some new technique we derive analytically formulas for the action of generators of algebra in this base (the were not known before). These formula turn out to be much more difficult than the formulas for the action of generators in the Gelfand-Tsetlin type base constructed by Molev.
