Geodesic
Noncommutative Symmetric Hall-Littlewood Polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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Noncommutative symmetric functions have many properties analogous to those of classical (commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the classical Schur basis) expand positively in noncommutative monomial basis. More of the classical properties extend to noncommutative setting as I will demonstrate introducing a new family of noncommutative symmetric functions, depending on one parameter. It seems to be an appropriate noncommutative analog of the Hall-Littlewood polynomials. 
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     author = {Tevlin, Lenny},
     title = {Noncommutative {Symmetric} {Hall-Littlewood} {Polynomials}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     year = {2011},
     doi = {10.46298/dmtcs.2964},
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Tevlin, Lenny. Noncommutative Symmetric Hall-Littlewood Polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2964. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2964/

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