Representations of $$E_6$$ E 6

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

Chapter Chapter 11 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 351-399 from Springer

Abstract: Abstract This chapter studies explicit representations of the simple Lie algebra of type $$E_6$$ E 6 . First we prove the cubic $$E_6$$ E 6 -generalization of the classical theorem on harmonic polynomials. Then we study the functor from the module category of $$D_5$$ D 5 to the module category of $$E_6$$ E 6 . Finally, we give a family of inhomogeneous oscillator representations of the simple Lie algebra of type $$E_6$$ E 6 on a space of exponential-polynomial functions and prove that their irreducibility is related to an explicit given algebraic variety.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-6391-6_11

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DOI: 10.1007/978-981-10-6391-6_11

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