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arXiv · 2311.06619

Irreducible representations of $\textrm{GL}_n(\mathbb{C})$ of minimal Gelfand-Kirillov dimension

Zhanqiang Bai·Yangyang Chen·Dongwen Liu·Binyong Sun
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Abstract

In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of $G=\textrm{GL}_n(\mathbb{C})$ possessing the minimal Gelfand-Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of $G$ of type $(n-1,1)$. We give the transition matrix between the two bases for the corresponding coherent families.

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Zhanqiang Bai, Yangyang Chen, Dongwen Liu, Binyong Sun. 2023-11-11. Irreducible representations of $\textrm{GL}_n(\mathbb{C})$ of minimal Gelfand-Kirillov dimension. https://arxiv.org/abs/2311.06619

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