Geodesic
Hopf Algebras from Branching Rules
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 177-192

Voir la notice de l'article provenant de la source Cambridge University Press

Below we work out the algebra structure of some Hopf algebras which arise concretely in restricting representations of the symmetric group to certain subgroups. The basic idea generalizes that used by Adams [1] for H *(BSU). The question arose in discussions with H. K. Farahat. I would like to thank him for his interest in the work and to acknowledge the usefulness of several stimulating conversations with him. 1. Review and statement of results. A homogeneous element of a graded abelian group will have its gradation referred to as its dimension. In all such groups below there will be no non-zero elements with negative or odd dimension. A graded algebra (resp. coalgebra) will be associative (resp. coassociative), strictly commutative (resp. co-commutative) and in dimension zero will be isomorphic to the ground ring F, providing the unit (resp. counit). We shall deal amost entirely with F = Z or F = Z/p for a prime p; the cases F = 0 or a localization of Z will occur briefly. In every case, the component in each dimension will be a finitely generated free F-module, so dualization works simply. 
Hoffman, P. Hopf Algebras from Branching Rules. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 177-192. doi: 10.4153/CJM-1983-012-1
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