The Gelfand-Kirillov dimension of a unitary highest weight module
Bai ZhanQiang1; Hunziker, Markus2
AbstractDuring the last decade, a great deal of activity has been devoted to the calculation of the Hilbert-Poincar, series of unitary highest weight representations and related modules in algebraic geometry. However, uniform formulas remain elusive-even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring (in the dual pair setting) and is inspired by Wang's formula for the dimension of a minimal nilpotent orbit.
Keywordunitary highest weight module associated variety Gelfand-Kirillov dimension nilpotent orbit
Funding ProjectNational Natural Science Foundation of China[11171324] ; Hong Kong Research Grants Council under RGC Project[60311] ; Hong Kong University of Science and Technology[DAG S09/10.SC02]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000365692100002
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Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
2.Baylor Univ, Dept Math, Waco, TX 76798 USA
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GB/T 7714
Bai ZhanQiang,Hunziker, Markus. The Gelfand-Kirillov dimension of a unitary highest weight module[J]. SCIENCE CHINA-MATHEMATICS,2015,58(12):2489-2498.
APA Bai ZhanQiang,&Hunziker, Markus.(2015).The Gelfand-Kirillov dimension of a unitary highest weight module.SCIENCE CHINA-MATHEMATICS,58(12),2489-2498.
MLA Bai ZhanQiang,et al."The Gelfand-Kirillov dimension of a unitary highest weight module".SCIENCE CHINA-MATHEMATICS 58.12(2015):2489-2498.
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