Gelfand-Kirillov Dimensions of the Z2-graded Oscillator Representations of sl(n)

• 作 者: Zhan Qiang BAI
• 机 构: Institute of Mathematics, Academy of Mathematics and System Sciences,Chinese Academy of Sciences,
• 出 处: Acta Mathematica Sinica
• 发表日期: 2015年06期
• 关键词: Gelfand-Kirillov dimension highest-weight module associated variety minimal GK-d

We find an exact formula of Gelfand–Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n, F)-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand–Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl (n, F) -modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and absolutely pointed modules.