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Journal of Lie Theory 19 (2009), No. 3, 507--525
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

First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type Bn), 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.

Keywords: Multisymmetric polynomials, reflection groups, polynomial invariant, second fundamental theorem, ideal of relations, trace identities.

MSC: 13A50, 14L30, 20G05

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