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Irreducible Representations of GLn(ℂ) of Minimal Gelfand–Kirillov Dimension

  • 期刊论文

  • 发表日期：

    2024年3月15日

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  • Zhan Qiang Bai,
  • Yang Yang Chen,
  • Dong Wen Liu,
  • Bin Yong Sun

摘要

In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of G = GLn(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.