Abstract
The research of Kac-Moody algebras breaks into two parts: structure theory and representation theory. This paper concentrates on the second part, In section one, we investigate the inclusion relation of weight sets of different modules and the comparison of weight multiplicities in a module. In section two, we discuss the maximal weights and weight strings in a module. As consequences, we prove some properties of roots for Kac-Moody algebras.
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