论文标题
正交谎言代数和组合身份的完整保形振荡器表示
Full Conformal Oscillator Representations of Orthogonal Lie Algebras and Combinatorial Identities
论文作者
论文摘要
Zhao和第二作者（2013）从O（k）-mod到O（k + 2）-mod的函数。在本文中，我们依次使用函子来获得通用的一阶差分操作员实现，以实现（2n + 3）在（n + 1）^2变量中的O（2n + 3）和N（n + 1）变量中的O（n + 1）变量的任何最高体重表示。当最高重量是主要积分时，我们会明确确定相应的有限维不可约的模块。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。我们还找到一个计算不可还原O（K + 2） - 模块的尺寸的方程式，以某些不可减至的O（k）模型的尺寸的交替总和。在Steinberg模块的情况下，我们获得了经典类型的新组合身份。
Zhao and the second author (2013) constructed a functor from o(k)-Mod to o(k + 2)-Mod. In this paper, we use the functor successively to obtain an universal first-order differential operator realization for any highest-weight representation of o(2n + 3) in (n + 1)^2 variables and that of o(2n + 2) in n(n + 1) variables. When the highest weight is dominant integral, we determine the corresponding finite-dimensional irreducible module explicitly. 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. We also find an equation of counting the dimension of an irreducible o(k + 2)-module in terms of certain alternating sum of the dimensions of irreducible o(k)-modules. In the case of the Steinberg modules, we obtain new combinatorial identities of classical type.
