Geodesic
A Lift of the Schur and Hall–Littlewood Bases to Non-commutative Symmetric Functions
Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 525-565

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DOI

We introduce a new basis of the algebra of non-commutative symmetric functions whose images under the forgetful map are Schur functions when indexed by a partition. Dually, we build a basis of the quasi-symmetric functions that expand positively in the fundamental quasi-symmetric functions. We then use the basis to construct a non-commutative lift of the Hall–Littlewood symmetric functions with similar properties to their commutative counterparts.
DOI : 10.4153/CJM-2013-013-0
Mots-clés : 05E05, Hall-Littlewood polynomial, symmetric function, quasisymmetric function, tableau 
Berg, Chris; Bergeron, Nantel; Saliola, Franco; Serrano, Luis; Zabrocki, Mike. A Lift of the Schur and Hall–Littlewood Bases to Non-commutative Symmetric Functions. Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 525-565. doi: 10.4153/CJM-2013-013-0
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     title = {A {Lift} of the {Schur} and {Hall{\textendash}Littlewood} {Bases} to {Non-commutative} {Symmetric} {Functions}},
     journal = {Canadian journal of mathematics},
     pages = {525--565},
     year = {2014},
     volume = {66},
     number = {3},
     doi = {10.4153/CJM-2013-013-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-013-0/}
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