Full Conformal Oscillator Representations of o(2n + 2) and Combinatorial Identities

作     者：Zhenyu ZHOU 

作者机构：Chern Institute of Mathematics and LPMCNankai University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Nankai Zhide Foundation 

摘      要：Zhao and Xu (2013) constructed a functor from o(n)-Mod to o(n+2)-Mod. In this paper,we use the functor successively to obtain full conformal oscillator representation of o(2n+2) in n(n+1)variables and determine the corresponding finite-dimensional irreducible module explicitly when the highest weight is dominant integral. We also find an equation of counting the dimension of an irreducible o(2n+2)-module in terms of certain alternating sum of the dimensions of irreducible o(2n)-modules, which leads to a new combinatorial identities of classical type in the case of the Steinberg modules. One can use the results to study tensor decomposition of finite-dimensional irreducible modules by solving certain first-order linear partial differential equations, and thereby obtain the corresponding physically interested ClebschGordan coefficients and exact solutions of Knizhnik-Zamolodchikov equation in WZW model of conformal field theory.