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Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
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Atsumu Sasaki
Published/Copyright:
September 21, 2010
Abstract
A holomorphic action of a Lie group G on a connected complex manifold D is called strongly visible with slice S if G · S is open in D and if there exists an antiholomorphic diffeomorphism σ of D preserving each G-orbit in D such that σ|s = ids. This paper deals with the non-symmetric spherical variety SO(8, ℂ)/G2(ℂ). We prove that a maximal compact subgroup of SO(8, ℂ) acts on SO(8, ℂ)/G2(ℂ) in a strongly visible fashion. Moreover, we can take a slice to be of dimension three which coincides with the rank of this spherical variety.
Keywords.: Complex manifold; visible actions; slice; spherical variety; multiplicity-free representation; Cayley algebra; universal covering space
Received: 2010-04-30
Revised: 2010-07-28
Published Online: 2010-09-21
Published in Print: 2011-September
© de Gruyter 2011
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- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
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Keywords for this article
Complex manifold;
visible actions;
slice;
spherical variety;
multiplicity-free representation;
Cayley algebra;
universal covering space
Articles in the same Issue
- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
- Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
