# 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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Cited literature [13 references]

https://hal.inria.fr/hal-01186281
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• HAL Id : hal-01186281, version 1

### Citation

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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