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A Schur-like basis of \(\mathsf{NSym}\) defined by a Pieri rule
The electronic journal of combinatorics, Tome 21 (2014) no. 3
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Recent research on the algebra of non-commutative symmetric functions and the dual algebra of quasi-symmetric functions has explored some natural analogues of the Schur basis of the algebra of symmetric functions. We introduce a new basis of the algebra of non-commutative symmetric functions using a right Pieri rule. The commutative image of an element of this basis indexed by a partition equals the element of the Schur basis indexed by the same partition and the commutative image is $0$ otherwise. We establish a rule for right-multiplying an arbitrary element of this basis by an arbitrary element of the ribbon basis, and a Murnaghan-Nakayama-like rule for this new basis. Elements of this new basis indexed by compositions of the form $(1^n, m, 1^r)$ are evaluated in terms of the complete homogeneous basis and the elementary basis.
DOI : 10.37236/3857
Classification : 05E05, 05A05, 05A17
Mots-clés : non-commutative symmetric functions, Pieri rules, Schur basis

John Maxwell Campbell  1   ; Karen Feldman  1   ; Jennifer Light  1   ; Pavel Shuldiner  1   ; Yan Xu  1

1 York University 
@article{10_37236_3857,
     author = {John Maxwell Campbell and Karen Feldman and Jennifer Light and Pavel Shuldiner and Yan Xu},
     title = {A {Schur-like} basis of {\(\mathsf{NSym}\)} defined by a {Pieri} rule},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {3},
     doi = {10.37236/3857},
     zbl = {1301.05357},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3857/}
}
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John Maxwell Campbell; Karen Feldman; Jennifer Light; Pavel Shuldiner; Yan Xu. A Schur-like basis of \(\mathsf{NSym}\) defined by a Pieri rule. The electronic journal of combinatorics, Tome 21 (2014) no. 3. doi: 10.37236/3857

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