Classification of reductive real spherical pairs II. The semisimple case

Knop F, Krötz B, Pecher T, Schlichtkrull H (2019)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2019

Journal

DOI: 10.1007/s00031-019-09515-w

Abstract

If 𝔤 is a real reductive Lie algebra and 𝔥⊂𝔤 is a subalgebra, then the pair (𝔥,𝔤) is called real spherical provided that 𝔤=𝔥+𝔭 for some choice of a minimal parabolic subalgebra 𝔭⊂𝔤. This paper concludes the classification of real spherical pairs (𝔥,𝔤), where 𝔥 is a reductive real algebraic subalgebra. More precisely, we classify all such pairs which are strictly indecomposable, and we discuss (in Section 6) how to construct from these all real spherical pairs. A preceding paper treated the case where 𝔤 is simple. The present work builds on that case and on the classification by Brion and Mikityuk for the complex spherical case.

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APA:

Knop, F., Krötz, B., Pecher, T., & Schlichtkrull, H. (2019). Classification of reductive real spherical pairs II. The semisimple case. Transformation Groups. https://dx.doi.org/10.1007/s00031-019-09515-w

MLA:

Knop, Friedrich, et al. "Classification of reductive real spherical pairs II. The semisimple case." Transformation Groups (2019).

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