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

Abstract

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