
Journal of Lie Theory 19 (2009), No. 3, 507525 Copyright Heldermann Verlag 2009 Vector Invariants of a Class of Pseudoreflection Groups and Multisymmetric Syzygies Mátyás Domokos Rényi Institute of Mathematics, Hungarian Academy of Sciences, P. O. Box 127, 1364 Budapest, Hungary domokos@renyi.hu First and second fundamental theorems are given for polynomial invariants of a class of pseudoreflection 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 byproduct. The algebra of multisymmetric polynomials over an arbitrary base ring is revisited. Keywords: Multisymmetric polynomials, reflection groups, polynomial invariant, second fundamental theorem, ideal of relations, trace identities. MSC: 13A50, 14L30, 20G05 [ Fulltextpdf (224 KB)] for subscribers only. 