Journal of Lie Theory

no. 3
Vector Invariants of a Class of Pseudoreflection Groups and Multisymmetric Syzygies
Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 507-525
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.
DOI: 10.5802/jolt.565
Classification: 13A50, 14L30, 20G05
Keywords: Multisymmetric polynomials, reflection groups, polynomial invariant, second fundamental theorem, ideal of relations, trace identities 
@article{JOLT_2009_19_3_a3,
     author = {M. Domokos},
     title = {Vector {Invariants} of a {Class} of {Pseudoreflection} {Groups} and {Multisymmetric} {Syzygies}},
     journal = {Journal of Lie Theory},
     pages = {507--525},
     year = {2009},
     volume = {19},
     number = {3},
     doi = {10.5802/jolt.565},
     zbl = {1221.13007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.565/}
}
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M. Domokos. Vector Invariants of a Class of Pseudoreflection Groups and Multisymmetric Syzygies. Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 507-525. doi: 10.5802/jolt.565

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