Computing equivariant matrices on homogeneous spaces for geometric deep learning and automorphic Lie algebras

Vincent Knibbeler*

*Corresponding author for this work

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Abstract

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.
Original languageEnglish
Article number27
JournalAdvances in Computational Mathematics
Volume50
Issue number2
DOIs
Publication statusPublished - 11 Apr 2024

Keywords

  • 16Z05
  • Equivariant convolutional kernels
  • Automorphic Lie algebras
  • 53Z50
  • Homogeneous space
  • 43A85
  • 68T07
  • Geometric frobenius reciprocity
  • Geometric deep learning

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