• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.481-492
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• 2000

As an application of Clifford theory, we are interested in a situation in which every irreducible projective character of a finite group G is an induced character of an irreducible linear character of some subgroup H of G. For this purpose, we study relative projective monomial groups with respect to subgroups.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.453-467
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• 2005

Let K be an algebraic number field. If k is the maximal cyclotomic subextension in K then the Schur K-group S(K) is obtained from the Schur k-group S(k) by scalar extension. In the paper we study projective Schur group PS(K) which is a generalization of Schur group, and prove that a projective Schur K-algebra is obtained by scalar extension of a projective Schur k-algebra where k is the maximal radical extension in K with mild condition.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.1-11
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• 2002

A Schur algebra was generalized to projective Schur algebra by admitting twisted group algebra. A Schur algebra is a projective Schur algebra with trivial 2-cocycle. In this paper we study situations that Schur algebra is a projective Schur algebra with nontrivial cocycle, and we find a criterion for a projective Schur algebra to be a Schur algebra.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.365-386
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• 2005

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.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.325-337
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• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.