Lam, Thomas; Lauve, Aaron; Sottile, Frank Skew Littlewood-Richardson rules from Hopf algebras. (English) Zbl 1243.16035 Int. Math. Res. Not. 2011, No. 6, 1205-1219 (2011). Summary: We use Hopf algebras to prove a version of the Littlewood-Richardson rule for skew Schur functions, which implies a conjecture of S. H. Assaf and P. R. W. McNamara [J. Comb. Theory, Ser. A 118, No. 1, 277-290 (2011; Zbl 1291.05205)]. 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. Cited in 1 ReviewCited in 10 Documents MSC: 16T05 Hopf algebras and their applications 05E05 Symmetric functions and generalizations 14M15 Grassmannians, Schubert varieties, flag manifolds Keywords:dual Hopf algebras; skew Schur functions; skew Littlewood-Richardson rules; ribbon Schur functions; skew Pieri rules; affine Grassmannians Citations:Zbl 1291.05205 PDFBibTeX XMLCite \textit{T. Lam} et al., Int. Math. Res. Not. 2011, No. 6, 1205--1219 (2011; Zbl 1243.16035) Full Text: DOI arXiv