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Gelfand-Kirillov dimensions of the $Z^2$-graded oscillator representations of sl(n)

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n, F)-modules that appeared in the Z^2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.

preprint2015arXivOpen access
Zhanqiang Bai
math.RT
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Zhanqiang Bai

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