Howe Duality For General Linear Lie Color Algebras

This paper is devoted to the study of Howe duality for general linear Lie color algebras.Taking advantage of Schur duality between(?)(m|n),the general linear Lie superalgebra,and the symmetric group(?),along with the connection between the representations of Lie color algebras and those of Lie superalgebras,Dongho Moon proved Schur duality between(?)(V,?),the general linear Lie color algebra,and the symmetric group(?)(See[13]).By using the method of "combining" two Schur dualities together and some properties of the Specht modules of the symmetric group(?)k,we show both Howe duality and skew Howe duality for(?)(V,?)and(?)(W,?)in this paper.