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

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