标题： 关于ISL(n,R)群的卡拉西奥多尔和其代数分解 显示英文标题

标题： On the Casimir of the group ISL(n,R) and its algebraic decomposition

摘要： 在本文中，提出了非齐次群ISL(n,R)在其包络代数中的Casimir算子（或Casimir不变量）的显式表达式，该表达式通过生成算子P^{rho}和E^{nu}{mu} 的张量指标的收缩可以以如下形式表示（稍更易理解为方程(1)）。 通过对此表达式进行对称化得到Casimir。 这种张量形式在仿射引力规范理论中粒子的分类中有用；例如基于ISL(4,R)的理论。 还证明了ISL(n,R)的Casimir可以表示为其小群的Casimirs的组合，这是后续构造其不可约表示的关键点。 显示英文摘要

摘要： In this paper, an explicit expression for the Casimir operator (or the Casimir invariant) of the inhomogeneous group ISL(n,R) in its enveloping algebra is proposed, which using contractions of the tenso- rial indices of the generating operators P^{rho} and E^{nu}{mu} may be presented in the following (slightly more comprehensible as equation (1)) form. The Casimir is obtained by symmetrizing this expression. This tensor form is useful in the classification of particles in affine gravitational gauge theories; such as that based on ISL(4,R). It is also proven that the Casimir of ISL(n,R) can be decomposed in terms of the Casimirs of its little groups, a key point in the posterior construction of its irreducible representations.