Weyl Group Invariants and Application to Spherical Harmonic Analysis on Symmetric Spaces

Details Weyl Group Invariants and Application to Spherical Harmonic Analysis on Symmetric Spaces Weyl Group Invariants and Application to Spherical Harmonic Analysis on Symmetric Spaces

2009-01-29

arxiv.org/abs/0901.4765v2

Mathematics

Representation Theory

Improved description of function spaces on the direct limit of compact symmetric spaces; updated references

Scientific paper

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/injective limits, specifically to theorems of Paley--Wiener type.

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