Representations of $$E_7$$ E 7

Xiaoping Xu ()
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Xiaoping Xu: Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics

Chapter Chapter 12 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 401-478 from Springer

Abstract: Abstract Explicit representations of the simple Lie algebra of type $$E_7$$ E 7 are given . 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 $$E_7$$ E 7 into a sum of irreducible submodules. Then we study the functor from the module category of $$E_6$$ E 6 to the module category of $$E_7$$ E 7 developed. Moreover, we construct a family of irreducible inhomogeneous oscillator representations of the simple Lie algebra of type $$E_7$$ E 7 on a space of exponential-polynomial functions, related to an explicitly given algebraic variety.

Date: 2017
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DOI: 10.1007/978-981-10-6391-6_12

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