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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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참고문헌 (35)
참고문헌 신청
/ 19001968 / Sitzungsberichteder Koniglich Preussischen Akademie der Wissenschaften zu Berlin : 148 ~ 166
/ 1901. / Uber eine Klasse von Matrizen reprinted in Gessamelte Abhandlungen 1
/ 1944 / The fre Lie ring and Lie representations of the full linear group 56 : 528 ~ 536
/ 1977 / Lie superalgebras 26 (1) : 8 ~ 96
/ 1986. / Cohomology of innite dimensional Lie algebras
/ 1901. / Uber eine Klasse von Matrizen reprinted in Gessamelte Abhandlungen 1
/ 1944 / The fre Lie ring and Lie representations of the full linear group 56 : 528 ~ 536
/ 1977 / Lie superalgebras 26 (1) : 8 ~ 96
/ 1986. / Cohomology of innite dimensional Lie algebras
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