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Noncommutative Symmetric Hall-Littlewood Polynomials

Abstract : 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.
Keywords : symmetric functions
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Lenny Tevlin. Noncommutative Symmetric Hall-Littlewood Polynomials. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.915-926, ⟨10.46298/dmtcs.2964⟩. ⟨hal-01215064⟩

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