Multiplicity-free primitive ideals associated with rigid nilpotent orbits

摘要: Let G be a simple algebraic group defined over ℂ. e nilpotent element in \( \mathfrak{g} \) = Lie(G) and denote by U (\( \), e) the finite W-algebra associated with pair e). It is known that component Γ of centraliser acts on set ℰ all one-dimensional representations In this paper we prove fixed point ℰΓ non-empty. As corollary, W-algebras admit representations. case rigid elements exceptional Lie algebras find irreducible highest weight \)-modules whose annihilators \)) come from via Skryabin’s equivalence. consequence, show for any orbit \mathcal{O} there exists multiplicity-free (and hence completely prime) primitive ideal variety equals Zariski closure \).