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

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The Kempf-Ness theorem provides a 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 enable representation decomposition into nested normal subgroup chains. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22245168

September 2, 2026Open Access

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

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Key Points

To examine geometric criteria for closed orbits under reductive group actions and explore representation decomposition techniques using plethysm and Clifford theory.
Formulated variational criteria linking Kempf–Ness stability to critical points of a norm-squared moment map on Kähler manifolds.
Applied gradient flow analysis to demonstrate convergence to unique closed orbit representatives.
Utilized Schur function plethysm and Clifford theory induction along nested normal subgroup chains.
Proved that an orbit of a reductive group is closed if and only if it contains a critical point of the norm-squared moment map.
Established that gradient flow along the norm-squared moment map converges to a unique representative for each closed orbit.
Characterized module induction from normal subgroups as decomposing into projective representations governed by degree-two cohomology classes.

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Implication

Mathematical analysis demonstrates closed orbit stability criteria under reductive group actions, indicating algebraic pathways for representation decomposition via Clifford theory and plethysm.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9a860d5d9e33f25c631908 https://doi.org/10.5281/zenodo.22245168

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

Key Points

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Implication

Discussion

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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