Sobolev Lifting over Invariants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Parusiński, Adam, Rainer, Armin
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211312
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Sobolev Lifting over Invariants. Adam Parusiński and Armin Rainer. SIGMA 17 (2021), 037, 31 pages

We prove lifting theorems for complex representations 𝑉 of finite groups 𝐺. Let σ = (σ₁,…, σₙ) be a minimal system of homogeneous basic invariants and let 𝑑 be their maximal degree. We prove that any continuous map 𝑓 ̅ : ℝᵐ → 𝑉 such that 𝑓 = σ ∘ 𝑓 ̅ is of class 𝐶ᵈ⁻¹'¹ is locally of Sobolev clas...