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Mathematics > Combinatorics

arXiv:math/0002073 (math)
[Submitted on 10 Feb 2000 (v1), last revised 21 Jul 2000 (this version, v2)]

Title:Non-commutative Pieri operators on posets

Authors:Nantel Bergeron (York University, Toronto Canada), Stefan Mykytiuk (York U.), Frank Sottile (University of Massachusetts), Stephanie van Willigenburg (York U)
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Abstract: We consider graded representations of the algebra NC of noncommutative symmetric functions on the Z-linear span of a graded poset P. The matrix coefficients of such a representation give a Hopf morphism from a Hopf algebra HP generated by the intervals of P to the Hopf algebra of quasi-symmetric functions. This provides a unified construction of quasi-symmetric generating functions from different branches of algebraic combinatorics, and this construction is useful for transferring techniques and ideas between these branches. In particular we show that the (Hopf) algebra of Billera and Liu related to Eulerian posets is dual to the peak (Hopf) algebra of Stembridge related to enriched P-partitions, and connect this to the combinatorics of the Schubert calculus for isotropic flag manifolds.
Comments: LaTeX 2e, 22 pages Minor corrections, updated references. Complete and final version, to appear in issue of J. Combin. Th. Ser. A dedicated to G.-C. Rota
Subjects: Combinatorics (math.CO); Quantum Algebra (math.QA); Rings and Algebras (math.RA)
MSC classes: 05E15, 05E05, 14M15, 05A15, 06A07, 16W30
Cite as: arXiv:math/0002073 [math.CO]
  (or arXiv:math/0002073v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.math/0002073
Journal reference: J. Combin. Th. Ser. A, Vol. 91, No. 1/2, Aug 2000, pp. 84-110
Related DOI: https://doi.org/10.1006/jcta.2000.3090

Submission history

From: Frank Sottile [view email]
[v1] Thu, 10 Feb 2000 16:19:37 UTC (24 KB)
[v2] Fri, 21 Jul 2000 17:14:08 UTC (24 KB)
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