Kempf–Ness Stability via Moment Maps and Representation Decomposition — E8 Intelligence Research

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The Kempf-Ness theorem provides a variational and geometric criterion for closed orbits in reductive group actions by linking stability to critical points of a norm-squared moment map, while plethysm and Clifford theory extend representation decomposition into nested normal subgroup chains. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22245167

September 2, 2026Open Access

Kempf–Ness Stability via Moment Maps and Representation Decomposition — E8 Intelligence Research

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Key Points

Characterize closed orbit stability in reductive group actions and analyze representation decomposition using plethysm and Clifford theory.
Analyzed the Kempf–Ness theorem for reductive group actions on Kähler manifolds using the gradient flow of squared moment map norms.
Evaluated plethysm via Schur function composition to decompose symmetric powers into irreducible representations of general linear groups.
Applied Clifford theory to decompose induced modules across normal subgroup chains using projective representations and second cohomology classes.
Demonstrated that a reductive group orbit is closed if and only if it contains a critical point of the norm-squared moment map.
Showed that gradient flow of the squared moment map norm converges to a unique closed orbit representative.
Formulated representation decompositions along nested normal subgroup chains via projective representations with specific two-cocycles.

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Implication

Mathematical study demonstrates orbit stability via moment map critical points and representation decomposition across subgroup chains, highlighting geometric criteria for reductive group actions.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9ab0dc5d9e33f25c631ed2 https://doi.org/10.5281/zenodo.22245167

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Kempf–Ness Stability via Moment Maps and Representation Decomposition — E8 Intelligence Research

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Cite This Study

Kempf–Ness Stability via Moment Maps and Representation Decomposition — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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