We develop an elementary method to compute spaces of equivariant maps from a homogeneous space G/H of a Lie group G to a module of this group. The Lie group is not required to be compact. More generally, we study spaces of invariant sections in homogeneous vector bundles, and take a special interest in the case where the fibres are algebras. These latter cases have a natural global algebra structure. We classify these automorphic algebras for the case where the homogeneous space has compact stabilisers. This work has applications in the theoretical development of geometric deep learning and also in the theory of automorphic Lie algebras.

中文翻译：

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计算几何深度学习和自同构李代数的齐次空间上的等变矩阵

我们开发了一种基本方法来计算从李群G的齐次空间G / H到该群的模的等变映射空间。李群不要求是紧的。更一般地说，我们研究齐次向量丛中的不变截面空间，并对纤维是代数的情况特别感兴趣。后一种情况具有自然的全局代数结构。我们针对齐次空间具有紧稳定子的情况对这些自守代数进行分类。这项工作在几何深度学习的理论发展以及自守李代数理论中都有应用。