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Gelfand–Kirillov Dimensions of the Z^2-graded Oscillator Representations of sl(n)

Gelfand–Kirillov Dimensions of the Z^2-graded Oscillator Representations of sl(n)
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摘要 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.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors 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.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors
作者 Zhan Qiang BAI
机构地区 Institute of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第6期921-937,共17页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China(Grant No.11171324)
关键词 Gelfand-Kirillov dimension highest-weight module associated variety minimal GKdimension module universal enveloping algebra Gelfand-Kirillov dimension highest-weight module associated variety minimal GKdimension module universal enveloping algebra
分类号 TN752 [电子电信—电路与系统]
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Acta Mathematica Sinica,English Series
2015年 第6期

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