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

Abstract

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.

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

References in corpus (4)

• Rings of continuous functions, symmetric products, and Frobenius algebras
• Multisymmetric syzygies
• Conjectures on the ring of commuting matrices
• Fundamental theorems for invariants of a class of pseudo-reflection groups

Cited by in corpus (3)

• Quarter-BPS states, multi-symmetric functions and set partitions
• Tensor Products of Quiver Bundles
• Multisymmetric polynomials in dimension three