Representations of E-7, equivalent combinatorics and algebraic varieties

doi:10.1142/S0219498818500457

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	Representations of E-7, equivalent combinatorics and algebraic varieties
	Xu, Xiaoping1,2
	2018-03-01
发表期刊	JOURNAL OF ALGEBRA AND ITS APPLICATIONS
ISSN	0219-4988
卷号	17 期号:3 页码:22
摘要	In our earlier work on a new functor from E-6-Mod to E-7-Mod, we found a oneparameter (c) family of inhomogeneous first-order differential operator representations of the simple Lie algebra of type E-7 in 27 variables. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector (a) over right arrow epsilon C-27 \{(0) over right arrow}, we prove that the space forms an irreducible E-7-module for any c epsilon C if (a) over right arrow is not on an explicitly given projective algebraic variety. Certain equivalent combinatorial properties of the basic oscillator representation of E-6 over its 27-dimensional module play key roles in our proof. Our result can also be used to study free bosonic field irreducible representations of the corresponding affine Kac-Moody algebra.
关键词	Inhomogeneous representation simple Lie algebra E-7 exponential-polynomial function equivalent combinatorics algebraic variety
DOI	10.1142/S0219498818500457
语种	英语
资助项目	NSFC[11671381] ; NSFC[11321101] ; Hua Loo-Keng Key Mathematical Laboratory, Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000424255100007
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29372
专题	数学所
通讯作者	Xu, Xiaoping
作者单位	1.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xiaoping. Representations of E-7, equivalent combinatorics and algebraic varieties[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS,2018,17(3):22.
APA	Xu, Xiaoping.(2018).Representations of E-7, equivalent combinatorics and algebraic varieties.JOURNAL OF ALGEBRA AND ITS APPLICATIONS,17(3),22.
MLA	Xu, Xiaoping."Representations of E-7, equivalent combinatorics and algebraic varieties".JOURNAL OF ALGEBRA AND ITS APPLICATIONS 17.3(2018):22.