TY - JOUR

T1 - Classification of reductive real spherical pairs II

T2 - the semisimple case

AU - Knop, F.

AU - Krötz, B.

AU - Pecher, T.

AU - Schlichtkrull, H.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062608213&partnerID=8YFLogxK

U2 - 10.1007/s00031-019-09515-w

DO - 10.1007/s00031-019-09515-w

M3 - Journal article

AN - SCOPUS:85062608213

VL - 24

SP - 467

EP - 510

JO - Transformation Groups

JF - Transformation Groups

SN - 1083-4362

IS - 2

ER -