KMS Of Academy of mathematics and systems sciences, CAS
The Gelfand-Kirillov dimension of a unitary highest weight module | |
Bai ZhanQiang1; Hunziker, Markus2 | |
2015-12-01 | |
发表期刊 | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
卷号 | 58期号:12页码:2489-2498 |
摘要 | During 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. |
关键词 | unitary highest weight module associated variety Gelfand-Kirillov dimension nilpotent orbit |
DOI | 10.1007/s11425-014-4968-y |
语种 | 英语 |
资助项目 | National 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研究方向 | Mathematics |
WOS类目 | Mathematics, Applied ; Mathematics |
WOS记录号 | WOS:000365692100002 |
出版者 | SCIENCE PRESS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/21403 |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Bai ZhanQiang |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Baylor Univ, Dept Math, Waco, TX 76798 USA |
推荐引用方式 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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