Gelfand-Kirillov Dimensions of the Z-graded Oscillator Representations of $\mathfrak{o}(n,\mathbb{C})$ and $\mathfrak{sp}(2n,\mathbb{C})$

Zhanqiang Bai

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arXiv · 1501.04781

Gelfand-Kirillov Dimensions of the Z-graded Oscillator Representations of $\mathfrak{o}(n,\mathbb{C})$ and $\mathfrak{sp}(2n,\mathbb{C})$

Zhanqiang Bai

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Abstract

In this paper, we compute the Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible $\mathfrak{o}(n, \mathbb{C})$-modules and $\mathfrak{sp}(2n, \mathbb{C})$-modules that appeared in the $\mathbb{Z}$-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. We also found that some of the modules have the secondly minimal GK-dimension, and some of them have the larger GK-dimension than the maximal GK-dimension of unitary highest-weight modules.

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BibTeX RIS

Zhanqiang Bai. 2015-01-20. Gelfand-Kirillov Dimensions of the Z-graded Oscillator Representations of $\mathfrak{o}(n,\mathbb{C})$ and $\mathfrak{sp}(2n,\mathbb{C})$. https://arxiv.org/abs/1501.04781

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