A classification of simple Lie modules having a 1-dimensional weight space

Britten, D. J.; Lemire, F. W.

doi:10.1090/S0002-9947-1987-0869228-9

A classification of simple Lie modules having a $1$-dimensional weight space
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Trans. Amer. Math. Soc. 299 (1987), 683-697 Request permission

Abstract:

Let $L$ denote a simple Lie algebra over the complex numbers. In this paper, we classify and construct all simple $L$ modules which may be infinite dimensional but have at least one $1$-dimensional weight space. This completes the study begun earlier by the authors for the case of $L = {A_n}$. The approach presented here relies heavily on the results of Suren Fernando whose dissertation dealt with simple weight modules and their weight systems.

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