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Skew Littlewood―Richardson rules from Hopf algebras

Abstract : We use Hopf algebras to prove a version of the Littlewood―Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood―Richardson rules for Schur $P-$ and $Q-$functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of the symplectic group.
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Thomas Lam, Aaron Lauve, Frank Sottile. Skew Littlewood―Richardson rules from Hopf algebras. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.355-366. ⟨hal-01186281⟩

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