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

We analyze the structure of the algebra $\mathbb{K}\langle \mathbf{x}\rangle^{\mathfrak{S}_n}$ of symmetric polynomials in non-commuting variables in so far as it relates to $\mathbb{K}[\mathbf{x}]^{\mathfrak{S}_n}$, its commutative counterpart. Using the "place-action'' of the symmet...

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Bibliographic Details

Published in:	Discrete Mathematics & Theoretical Computer Science
Main Authors:	François Bergeron, Aaron Lauve
Format:	Article
Language:	English
Published:	Discrete Mathematics & Theoretical Computer Science 2008-01-01
Subjects:	chevalley theorem symmetric group noncommutative symmetric polynomials set partitions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Online Access:	https://dmtcs.episciences.org/3606/pdf