Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
نویسنده
چکیده
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan [12]. The bases for this algebra are indexed by set partitions. We show that there exist a natural inclusion of the Hopf algebra of noncommutative symmetric functions studied in [17] in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials.
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