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arXiv · 1902.09497

Gelfand pairs admit an Iwasawa decomposition

Nicolas Monod
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Abstract

Every Gelfand pair (G,K) admits a decomposition G=KP, where P<G is an amenable subgroup. In particular, the Furstenberg boundary of G is homogeneous. Applications include the complete classification of non-positively curved Gelfand pairs, relying on earlier joint work with Caprace, as well as a canonical family of pure spherical functions in the sense of Gelfand--Godement for general Gelfand pairs.

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Nicolas Monod. 2019-02-25. Gelfand pairs admit an Iwasawa decomposition. https://arxiv.org/abs/1902.09497

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