论文标题
Gelfand-Tsetlin基座的功能实现
A functional realization of the Gelfand-Tsetlin base
论文作者
论文摘要
在论文中，我们考虑了lie代数$ \ mathfrak {gl} _n $在组$ gl_n $上的功能空间中的有限维度不可约表示。事实证明，与Gelfand-Tsetlin图相对应的功能是某些与$ a $ a $ a-hypheperric函数密切相关的新功能的线性组合。这些新功能是偏微分方程系统的解决方案，人们通过“反对称化”从Gelfand-Kapranov-Zelevinsky获得。构造的线性组合中的系数是超几何常数，即当代替所有参数时，它们是某些超小几幅函数的值。
In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin diagrams are linear combinations of some new functions of hypergeometric type which are closely related to $A$-hypergeometric functions. These new functions are solution of a system of partial differential equations which one obtains from the Gelfand-Kapranov-Zelevinsky by an "antisymmetrization". The coefficients in the constructed linear combination are hypergeometric constants i.e. they are values of some hypergeometric functions when instead of all arguments ones are substituted.
