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FREE LIE SUPERALGEBRAS AND THE REPRESENTATIONS OF gl(m; n) AND q(n)

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대한수학회 (The Korean Mathematical Society)|2005.03|대한수학회지 (Journal of the KMS)|제42권 제2호|pp. 365-386

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참고문헌

주제분류수학

초록

Abstract

Let L be the free Lie superalgebra generated by a Z2-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 homo-geneous 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) representa-tions of the symmetric groups.

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