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 Kählermanifold Z .More precisely, we suppose that the action of a compact Lie group with Lie algebra u extends holomorphically to an action of the complexified group U^C and that the U -action on Z is Hamiltonian. If G ⊂ U C is compatible, there is a corresponding gradient map μp : X → p, where g = k ⊕ 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

Stability, Analytic Stability for Real Reductive Lie Groups / Biliotti, Leonardo; Windare, OLUWAGBENGA JOSHUA. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - (In corso di stampa), pp. 1-31. [10.1007/s12220-022-01146-0]

Stability, Analytic Stability for Real Reductive Lie Groups

Biliotti Leonardo
;
Oluwagbenga Joshua Windare
In corso di stampa

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 Kählermanifold Z .More precisely, we suppose that the action of a compact Lie group with Lie algebra u extends holomorphically to an action of the complexified group U^C and that the U -action on Z is Hamiltonian. If G ⊂ U C is compatible, there is a corresponding gradient map μp : X → p, where g = k ⊕ 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
Stability, Analytic Stability for Real Reductive Lie Groups / Biliotti, Leonardo; Windare, OLUWAGBENGA JOSHUA. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - (In corso di stampa), pp. 1-31. [10.1007/s12220-022-01146-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2935312
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