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arXiv · 1501.04774

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

Zhanqiang Bai
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Abstract

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.

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BibTeXRIS

Zhanqiang Bai. 2015-01-20. Gelfand-Kirillov dimensions of the $Z^2$-graded oscillator representations of sl(n). https://arxiv.org/abs/1501.04774

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