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THE COEFFICIENT COALGEBRA OF A SYMMETRIZED TENSOR SPACE

By Randall R. Holmes and David P. Turner

Abstract

Abstract. The coefficient coalgebra of r-fold tensor space and its dual, the Schur algebra, are generalized in such a way that the role of the symmetric group Σr is played by an arbitrary subgroup of Σr. The dimension of the coefficient coalgebra of a symmetrized tensor space is computed and the dual of this coalgebra is shown to be isomorphic to the analog of the Schur algebra. Let K be the field of complex numbers. The vector space E = Kn is naturally viewed as a (left) module for the group algebra KΓ of the general linear group Γ = GLn(K). The r-fold tensor product E⊗r is in turn a module for KΓr, where Γr = Γ × · · · × Γ (r factors). Let G be a subgrou

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.2698
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