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- W1964908911 abstract "Abstract Let be a rational finite dimensional complex representation of a reductive linear algebraic group G , and let be a system of generators of the algebra of invariant poly- nomials ℂ[ V ] G . We study the problem of lifting mappings over the mapping of invariants . Note that ¾( V ) can be identified with the cate- gorical quotient V // G and its points correspond bijectively to the closed orbits in V . We prove that if f belongs to a quasianalytic subclass satisfying some mild closedness properties that guarantee resolution of singularities in 𝒞 e.g., the real analytic class, then f admits a lift of the same class 𝒞 after desingularization by local blow-ups and local power substitutions. As a consequence we show that f itself allows for a lift that belongs to SBV loc , i.e., special functions of bounded variation. If ρ is a real representation of a compact Lie group, we obtain stronger versions." @default.
- W1964908911 created "2016-06-24" @default.
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- W1964908911 date "2012-04-16" @default.
- W1964908911 modified "2023-09-26" @default.
- W1964908911 title "Lifting Quasianalytic Mappings over Invariants" @default.
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- W1964908911 doi "https://doi.org/10.4153/cjm-2011-049-0" @default.
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