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On Double Coset Decompositions of Real Reductive Groups for Reductive Absolutely Spherical Subgroups

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Geometric and Harmonic Analysis on Homogeneous Spaces and Applications (TJC 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 366))

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Abstract

The aim of this article is to show an induction argument to obtain the double coset decomposition \(H\backslash G/L\) of a real reductive Lie group G with respect to reductive absolutely spherical subgroups H and L. As an application, we describe generic double cosets with some exceptions. The exceptions for our approach come from some factorizations of type \({\text {D}}_{4}\)-groups.

This work was supported by a JSPS Kakenhi (70780063).

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Acknowledgements

The author would like to express his sincere gratitude to Professor Toshiyuki Kobayashi for his generous support and constant encouragement. He is also grateful to an anonymous referee for comments on this article.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Yuichiro Tanaka

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  1. Yuichiro Tanaka
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Correspondence to Yuichiro Tanaka .

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Editors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia

    Ali Baklouti

  2. Department of Mathematics, Osaka City University, Osaka, Japan

    Hideyuki Ishi

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Tanaka, Y. (2021). On Double Coset Decompositions of Real Reductive Groups for Reductive Absolutely Spherical Subgroups. In: Baklouti, A., Ishi, H. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications . TJC 2019. Springer Proceedings in Mathematics & Statistics, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-030-78346-4_14

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