A Theory of Stiefel Harmonics

Stephen Gelbart

Type: Article

Publication Date: 1974-05-01

Citations: 15

DOI: https://doi.org/10.2307/1996816

Abstract

An explicit theory of special functions is developed for the homogeneous space $SO(n)/SO(n - m)$ generalizing the classical theory of spherical harmonics. This theory is applied to describe the decomposition of the Fourier operator on $n \times m$ matrix space in terms of operator valued Bessel functions of matrix argument. Underlying these results is a hitherto unnoticed relation between certain irreducible representations of $SO(n)$ and the polynomial representations of $GL(m,{\mathbf {C}})$.

Locations

Transactions of the American Mathematical Society - View - PDF

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