论文标题
在GKZ超几何函数的矩阵元素表示上
On a matrix element representation of the GKZ hypergeometric functions
论文作者
论文摘要
我们开发了一种代表理论方法，用于研究Gelfand，Kapranov和Zelevisnky（GKZ）的广义高几何功能的研究。我们表明，可以使用振荡器类型的非还原性lie代数$ \ mathfrak {l} _n $的矩阵元素来识别GKZ高几何功能。 Whittaker功能与$ \ Mathfrak {gl} _ {\ ell+1}（\ Mathbb {r}）$的主体系列表示相关$ \ mathfrak {gl} _ {\ ell+1}（\ mathbb {r}）$，另一种矩阵元素表示$ \ mathfrak {l} _ {\ ell（\ ell（\ ell+1）} $。
We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may be identified with matrix elements of non-reductive Lie algebras $\mathfrak{L}_N$ of oscillator type. The Whittaker functions associated with principal series representations of $\mathfrak{gl}_{\ell+1}(\mathbb{R})$ being special cases of GKZ hypergeometric functions, thus admit along with a standard matrix element representations associated with reductive Lie algebra $\mathfrak{gl}_{\ell+1}(\mathbb{R})$, another matrix element representation in terms of $\mathfrak{L}_{\ell(\ell+1)}$.
