The algebra of differential geometry operations on symmetric tensors overconstant curvature manifolds forms a novel deformation of the sl(2,R)[semidirect product] R^2 Lie algebra. We present a simple calculus forcalculations in its universal enveloping algebra. As an application, we derivegenerating functions for the actions and gauge invariances of massive,partially massless and massless (for both bose and fermi statistics) higherspins on constant curvature backgrounds. These are formulated in terms of aminimal set of covariant, unconstrained, fields rather than towers of auxiliaryfields. Partially massless gauge transformations are shown to arise asdegeneracies of the flat, massless gauge transformation in one dimensionhigher. Moreover, our results and calculus offer a considerable simplificationover existing techniques for handling higher spins. In particular, we show howtheories of arbitrary spin in dimension d can be rewritten in terms of a singlescalar field in dimension 2d where the d additional dimensions correspond tocoordinate differentials. We also develop an analogous framework forspinor-tensor fields in terms of the corresponding superalgebra.
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机译：在恒定曲率流形上的对称张量上的微分几何运算的代数形成sl（2，R）[半直接乘积] R ^ 2 Lie代数的新型变形。我们在其通用包络代数中提出了一种简单的计算方法。作为一个应用程序，我们为恒定曲率背景下的大质量，部分无质量和无质量（对于玻色和费米统计）的高自旋的作用和尺度不变性生成函数。这些是根据一组最小的协变量，不受约束的字段而不是辅助字段的塔来制定的。已显示部分无质量的标量变换会在更高的一个维度上产生平坦无质量的标量变换的简并性。此外，我们的结果和演算比用于处理更高自旋的现有技术提供了相当大的简化。特别地，我们展示了如何可以在维度2d中的单个标量场方面重写维度d中的任意自旋的理论，其中d个附加维度对应于坐标微分。我们还根据相应的超代数为自旋张量场开发了一个类似的框架。
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