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Skew Littlewood-Richardson rules from Hopf algebras. (English) Zbl 1243.16035

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.

MSC:

16T05 Hopf algebras and their applications
05E05 Symmetric functions and generalizations
14M15 Grassmannians, Schubert varieties, flag manifolds

Citations:

Zbl 1291.05205
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