Abstract
ABSTRACTIn this paper, we give a method to compute the Gelfand–Kirillov dimensions of some polynomial–type weight modules. These modules are infinite-dimensional irreducible 𝔬(n,ℂ)-modules and 𝔰𝔭(2n,ℂ)-modules that appeared in the ℤ-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. We also found that some of these modules have the secondly minimal GK-dimension, and some of them have the larger GK-dimension than the maximal GK-dimension apearing in unitary highest-weight modules.
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