Group actions on p-adic symplectic manifolds

2025/12/17 by Crespo, Luis, Pelayo, Álvaro
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2512.15575

Abstract

Let p be a prime number. We introduce symplectic actions of p-adic analytic Lie groups on p-adic symplectic manifolds. Then we show that any p-adic symplectic action G×(M,ω)→(M,ω) has a momentum map μ:M→\mathfrakg^*, and that a proper p-adic symplectic action is Hamiltonian if and only if every orbit is isotropic. We conclude by defining p-adic symplectic toric manifolds, by analogy with the real case.

Citations

• Integrable systems with symmetries: toric, semitoric, and beyond
• Darboux's Theorem in p-adic symplectic geometry
• Rigidity and flexibility in p-adic symplectic geometry
• p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I
• Symplectic invariants of semitoric systems and the inverse problem for\n quantum systems
• Convexity of singular affine structures and toric-focus integrable Hamiltonian systems
• Hamiltonian and symplectic symmetries: an introduction
• Symplectic group and Heisenberg group in p-adic quantum mechanics
• Multifractals, Mumford curves, and Eternal Inflation
• Symplectic torus actions with coisotropic principal orbits
• p-Adic and Adelic Quantum Mechanics
• Symplectic Geometry

Related

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• A symplectic Hilbert-Smith conjecture
• Symplectic quotients and representability: the circle action case
• Hamiltonian and symplectic symmetries: an introduction
• Group-valued momentum maps for actions of automorphism groups