论文标题
$ \ mathfrak {o} _5 $的Gelfand-Tsetlin类型基础的功能方法
A functional approach to a Gelfand-Tsetlin type base for $\mathfrak{o}_5$
论文作者
论文摘要
在组$ spin_5 \ simeq sp_4 $上，在函数空间中，Lie代数$ \ Mathfrak {O} _5 $的表示形式实现。在表示形式中，我们采用与限制性$ \ mathfrak {o} _5 \ downarrow \ mathfrak {o} _3 $关联的Gelfand-Tsetlin类型基础。这样的基础是有用的，就是量子力学中出现的问题。我们在对应于基础向量的组上明确构建功能。与Lie代数$ \ MATHFRAK {GL} _3 $，$ \ MATHFRAK {SP} _4 $一样，这些功能可以通过$ a $ a $ a-hyphyphemementric函数表示（这在更高率的谴责中对这些系列的代数不满意）。使用此实现公式来获得发电机的作用。
A realization of representations of the Lie algebra $\mathfrak{o}_5$ in the space of functions on a group $Spin_5\simeq Sp_4$ is considered. In a representation we take a Gelfand-Tsetlin type base associated with a restriction $\mathfrak{o}_5\downarrow\mathfrak{o}_3$. Such a base is useful is problems appearing in quantum mechanics. We construct explicitely functions on the group that correspond to base vectors. As in the cases of Lie algebras $\mathfrak{gl}_3$, $\mathfrak{sp}_4$ these functions can be expressed through $A$-hypergeometric functions (this does not hold for algebras of these series in higher dimentions). Using this realization formulas for the action of generators are obtained.
