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- W4313887839 abstract "We presented a systematic treatment of a Hilbert criterion for stability theory for an action of a real reductive group G on a real submanifold X of a Kähler manifold Z. More precisely, we suppose that the action of a compact Lie group U with Lie algebra $${mathfrak {u}}$$ extends holomorphically to an action of the complexified group $$U^mathbb {C}$$ and that the U-action on Z is Hamiltonian. If $$Gsubset U^mathbb {C}$$ is compatible, there is a corresponding gradient map $$mu _{mathfrak {p}} : Xrightarrow {mathfrak {p}}$$ , where $${mathfrak {g}}= {mathfrak {k}}oplus {mathfrak {p}}$$ is a Cartan decomposition of the Lie algebra of G. The concept of energy complete action of G on X is introduced. For such actions, one can characterize stability, semistability and polystability of a point by a numerical criteria using a G-equivariant function called maximal weight. We also prove the classical Hilbert–Mumford criteria for semistability and polystability conditions." @default.
- W4313887839 created "2023-01-10" @default.
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- W4313887839 date "2023-01-09" @default.
- W4313887839 modified "2023-10-16" @default.
- W4313887839 title "Stability, Analytic Stability for Real Reductive Lie Groups" @default.
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- W4313887839 doi "https://doi.org/10.1007/s12220-022-01146-0" @default.
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