Partial Differential Equation Approach to E-7

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	Partial Differential Equation Approach to E-7
其他题名	Partial Differential Equation Approach to E_7
	Xu Xiao Ping
	2015
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	31 期号:2 页码:177-200
摘要	By solving certain partial differential equations, we find the explicit decomposition of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra E-7 into a sum of irreducible submodules. This essentially gives a partial differential equation proof of a combinatorial identity on the dimensions of certain irreducible modules of E-7. We also determine two three-parameter families of irreducible submodules in the solution space of Cartan's well-known fourth-order E-7-invariant partial differential equation.
其他摘要	By solving certain partial differential equations, we find the explicit decomposition of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra E_7 into a sum of irreducible submodules. This essentially gives a partial differential equation proof of a combinatorial identity on the dimensions of certain irreducible modules of E_7. We also determine two three-parameter families of irreducible submodules in the solution space of Cartan’s well-known fourth-order E_7-invariant partial differential equation.
关键词	E(7) E7 SYMMETRY ALGEBRA Simple Lie algebra E-7 partial differential equation irreducible module decomposition combinatorial identity
收录类别	CSCD
语种	英语
资助项目	[NSFC]
CSCD记录号	CSCD:5336534
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/55095
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Xu Xiao Ping. Partial Differential Equation Approach to E-7[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2015,31(2):177-200.
APA	Xu Xiao Ping.(2015).Partial Differential Equation Approach to E-7.ACTA MATHEMATICA SINICA-ENGLISH SERIES,31(2),177-200.
MLA	Xu Xiao Ping."Partial Differential Equation Approach to E-7".ACTA MATHEMATICA SINICA-ENGLISH SERIES 31.2(2015):177-200.