Representations of E-7, equivalent combinatorics and algebraic varieties | |
Xu, Xiaoping1,2 | |
2018-03-01 | |
Source Publication | JOURNAL OF ALGEBRA AND ITS APPLICATIONS |
ISSN | 0219-4988 |
Volume | 17Issue:3Pages:22 |
Abstract | 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. |
Keyword | Inhomogeneous representation simple Lie algebra E-7 exponential-polynomial function equivalent combinatorics algebraic variety |
DOI | 10.1142/S0219498818500457 |
Language | 英语 |
Funding Project | NSFC[11671381] ; NSFC[11321101] ; Hua Loo-Keng Key Mathematical Laboratory, Chinese Academy of Sciences |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000424255100007 |
Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/29372 |
Collection | 数学所 |
Affiliation | 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 |
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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