论文标题
特殊线性谎言代数和组合身份的完整射影振荡器表示
Full Projective Oscillator Representations of Special Linear Lie Algebras and Combinatorial Identities
论文作者
论文摘要
Zhao和第二作者（2011年）使用SL（N+1）和Shen的混合产品的投影振荡器表示形式，从SL（N）-mod到SL（N+1）-mod的SL（N）-mod构建了一个新函子。在本文中，我们从n = 2开始，并连续使用函子来获得SL（n+1）的任何有限维不可减少表示的完整射击振荡器实现。 SL（n+1）的所有根矢量的表示公式都是根据N（n+1）/2变量中的一阶差分运算符给出的。人们可以通过求解某些一阶线性偏微分方程方程来研究有限维模块的张量分解，从而获得了wzw模型模型的Gunizhik-Zamolodchikov方程的相应物理感兴趣的Clebsch-Gordan系数和精确的解决方案。
Using the projective oscillator representation of sl(n+1) and Shen's mixed product for Witt algebras, Zhao and the second author (2011) constructed a new functor from sl(n)-Mod to sl(n+1)-Mod. In this paper, we start from n = 2 and use the functor successively to obtain a full projective oscillator realization of any finite-dimensional irreducible representation of sl(n+1). The representation formulas of all the root vectors of sl(n+1) are given in terms of first-order differential operators in n(n+1)/2 variables. One can use the result to study tensor decompositions of finite-dimensional irreducible modules by solving certain first-order linear partial differential equations, and thereby obtain the corresponding physically interested Clebsch-Gordan coefficients and exact solutions of Knizhnik-Zamolodchikov equation in WZW model of conformal field theory.
