Polynomiality of invariants, unimodularity and adapted pairs

摘要: Let \( \mathfrak{a} \) be a finite-dimensional Lie algebra and Y\left( \right) the invariant subalgebra of its symmetric S\left( under adjoint action. Recently there has been considerable interest in studying situations when may polynomial on index generators, for example if is biparabolic or centralizer {\mathfrak{g}^x} semisimple \mathfrak{g} \).