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Representations of E-7, equivalent combinatorics and algebraic varieties
Xu, Xiaoping1,2
2018-03-01
Source PublicationJOURNAL OF ALGEBRA AND ITS APPLICATIONS
ISSN0219-4988
Volume17Issue:3Pages:22
AbstractIn 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.
KeywordInhomogeneous representation simple Lie algebra E-7 exponential-polynomial function equivalent combinatorics algebraic variety
DOI10.1142/S0219498818500457
Language英语
Funding ProjectNSFC[11671381] ; NSFC[11321101] ; Hua Loo-Keng Key Mathematical Laboratory, Chinese Academy of Sciences
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000424255100007
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29372
Collection数学所
Affiliation1.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
Recommended Citation
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.
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