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首页> 外文期刊>Journal of algebra and its applications >PATH HYPERGEOMETRIC FUNCTIONS
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PATH HYPERGEOMETRIC FUNCTIONS

机译：路径超基因组功能

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Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the solutions of the Calogero–Sutherland model. If n = 2, the master function of the trace function is exactly the classical Gauss hypergeometric function. When n > 2, the master functions of the trace functions are a new family of multiple hypergeometric functions, whose differential property and Euler type integral representation are dominated by certain polynomials of integral paths connecting pairs of positive integers. Moreover, we also find the trace functions for sp(2n) explicitly and prove that they give rise to solutions of the Olshanesky–Perelomov model of type C. The master functions of the trace functions for sp(2n) are similar new multiple path hypergeometric functions. Analogous multiple path hypergeometric functions for orthogonal Lie algebras are defined and studied.
机译：在一定条件下，我们找到了由Etingof结合Calogero-Sutherland模型的解引入的gl（n）-模块中某些纠缠算子的跟踪函数的显式。如果n = 2，则跟踪函数的主函数正好是经典的高斯超几何函数。当n> 2时，跟踪函数的主函数是一个新的多重超几何函数族，其微分性质和Euler型积分表示形式由连接正整数对的积分路径的某些多项式决定。此外，我们还明确找到了sp（2n）的跟踪函数，并证明它们引起了类型C的Olshanesky–Perelomov模型的求解。sp（2n）跟踪函数的主函数类似于新的多径超几何功能。定义并研究了正交李代数的类似多径超几何函数。

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