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Gelfand-Kirillov dimensions of the ℤ2-graded oscillator representations of \(\mathfrak{s}\mathfrak{l}\)(n)

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Abstract

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible \(\mathfrak{s}\mathfrak{l}\)(n, \(\mathbb{F}\))-modules that appeared in the ℤ2-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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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Zhan Qiang Bai

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  1. Zhan Qiang Bai
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Correspondence to Zhan Qiang Bai.

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Supported by National Natural Science Foundation of China (Grant No. 11171324)

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Bai, Z.Q. Gelfand-Kirillov dimensions of the ℤ2-graded oscillator representations of \(\mathfrak{s}\mathfrak{l}\)(n). Acta. Math. Sin.-English Ser. 31, 921–937 (2015). https://doi.org/10.1007/s10114-015-4237-1

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  • DOI: https://doi.org/10.1007/s10114-015-4237-1

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