• Published : 2005.02.01


Let L be the free Lie superalgebra generated by a $Z_2$-graded vector space V over C. Suppose that g is a Lie superalgebra gl(m, n) or q(n). We study the g-module structure on the kth homogeneous component Lk of L when V is the natural representation of g. We give the multiplicities of irreducible representations of g in Lk by using the character of Lk. The multiplicities are given in terms of the character values of irreducible (projective) representations of the symmetric groups.


free lie superalgebra;representation;character;general linear Lie superalgebra


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