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Representations of $$G_2$$ G 2 and $$F_4$$ F 4

In: Representations of Lie Algebras and Partial Differential Equations

Author

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  • Xiaoping Xu

    (Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics
    University of Chinese Academy of Sciences, School of Mathematics)

Abstract

We determine the structure of the canonical bosonic and fermionic oscillator representations of the simple Lie algebra of type $$G_2$$ G 2 over its 7-dimensional module. Moreover, we present a one-parameter family of conformal oscillator representations of $$G_2$$ G 2 derived from those of the simple Lie algebra of type $$B_3$$ B 3 and determine their irreducibility. Furthermore, we use partial differential equations to find the explicit irreducible decomposition of the space of polynomial functions on 26-dimensional basic irreducible module of the simple Lie algebra of type $$F_4$$ F 4 .

Suggested Citation

  • Xiaoping Xu, 2017. "Representations of $$G_2$$ G 2 and $$F_4$$ F 4," Springer Books, in: Representations of Lie Algebras and Partial Differential Equations, chapter 0, pages 329-349, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6391-6_10
    DOI: 10.1007/978-981-10-6391-6_10
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