Vector invariants of a class of pseudo-reflection groups and multisymmetric syzygies

Details Vector invariants of a class of pseudo-reflection groups and multisymmetric syzygies Vector invariants of a class of pseudo-reflection groups and multisymmetric syzygies

2007-06-14

arxiv.org/abs/0706.2154v1

Mathematics

Representation Theory

Joining the contents of math.RT/0602303v3 and math.RT/0611430v1 plus some additional material

Scientific paper

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. Special case of the result is a finite presentation of the algebra of multisymmetric polynomials. Reducedness of the invariant commuting scheme is proved as a by-product. The algebra of multisymmetric polynomials over an arbitrary base ring is revisited.

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