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
domokos@renyi.hu
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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