Vector invariants of a class of pseudoreflection groups and multisymmetric syzygies. (English) Zbl 1221.13007
Summary: First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type \(B_n\)), under the assumption that the order of the group is invertible in the base field. As a special case, a finite presentation of the algebra of multisymmetric polynomials is obtained. Reducedness of the invariant commuting scheme is proved as a by-product. The algebra of multisymmetric polynomials over an arbitrary base ring is revisited.
MSC:
13A50 | Actions of groups on commutative rings; invariant theory |
14L30 | Group actions on varieties or schemes (quotients) |
20G05 | Representation theory for linear algebraic groups |