Harmonic analysis on real reductive symmetric spaces

Details Harmonic analysis on real reductive symmetric spaces Harmonic analysis on real reductive symmetric spaces

2003-04-22

arxiv.org/abs/math/0304322v1

Proceedings of the ICM, Beijing 2002, vol. 2, 545--554

Mathematics

Representation Theory

Scientific paper

Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $\sigma$ be an involution of the Lie group $G$, $H$ an open subgroup of the subgroup of fixed points of $\sigma$. One decomposes the elements of $L^2(G/H)$ with the help of joint eigenfunctions under the algebra of left invariant differential operators under $G$ on $G/H$.

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