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Refinements of the Littlewood-Richardson rule

Abstract : We refine the classical Littlewood-Richardson rule in several different settings. We begin with a combinatorial rule for the product of a Demazure atom and a Schur function. Building on this, we also describe the product of a quasisymmetric Schur function and a Schur function as a positive sum of quasisymmetric Schur functions. Finally, we provide a combinatorial formula for the product of a Demazure character and a Schur function as a positive sum of Demazure characters. This last rule implies the classical Littlewood-Richardson rule for the multiplication of two Schur functions.
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J. Haglund, K. Luoto, S. Mason, S. van Willigenburg. Refinements of the Littlewood-Richardson rule. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.435-442, ⟨10.46298/dmtcs.2744⟩. ⟨hal-01185437⟩



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