• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.823-828
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• 1999

We extend the notion of category $O^g$ for Kac-Moody algebras to generalized Kac-Moody algebras and prove some analogues of results for Kac-Moody algebras.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.519-524
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• 1997

We extent the notion of equivalent relation $\approx$ for Kac-Moody algebras to generalized Kac-Moody algebras and prove some analogues of results for Kac-Moody algebras.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.559-581
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• 2013

This paper is motivated by a 2001 paper of Choie and Kim and a 2006 paper of Bump and Choie. The paper of Choie and Kim extends an earlier result of Bol for elliptic modular forms to the setting of Siegel and Jacobi forms. The paper of Bump and Choie provides a representation theoretic interpretation of the phenomenon, and shows how a natural generalization of Choie and Kim's result on Siegel modular forms follows from a natural conjecture regarding ($g$, K)-modules. In this paper, it is shown that the conjecture of Bump and Choie follows from work of Boe. A second proof which is along the lines of the proof given by Bump and Choie in the genus 2 case is also included, as is a similar treatment of the result of Choie and Kim on Jacobi forms.