Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables

Details Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables

2009-10-16

arxiv.org/abs/0910.3024v1

Mathematics

Combinatorics

14 pages

Scientific paper

We analyze the structure of the algebra N of symmetric polynomials in non-commuting variables in so far as it relates to its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of N analogous to the classical theorems of Chevalley, Shephard-Todd on finite reflection groups.

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