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Transactions of the American Mathematical Society

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Symmetries of spherical harmonics

Author: Roberto De Maria Nunes Mendes
Journal: Trans. Amer. Math. Soc. 204 (1975), 161-178
MSC: Primary 22E30; Secondary 43A90
MathSciNet review: 0357687
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Abstract: Let $ G$ be a group of linear transformations of $ {R^n}$ and $ {H_k}(G)$ the vector space of spherical harmonics invariant under $ G$. The Pálya function is the formal power series $ {\Sigma _{k \geq 0}}{t^k}\dim {H_k}(G)$. In this paper, after classifying all closed subgroups of $ O(4)$, we compute the Pólya functions for these groups. These functions have recently proved to be of interest in quantum mechanics and elementary particle physics.

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Keywords: Orthogonal group, generating function, spherical harmonic, closed subgroup, invariant
Article copyright: © Copyright 1975 American Mathematical Society