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Representations of Special Linear Algebras

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

First we present a fundamental lemma of solving flag partial differential equations for polynomial solutions. Then we present the canonical bosonic and fermionic oscillator representations of type A over their minimal natural modules and minimal orthogonal modules. Moreover, we determine the structure of the noncanonical oscillator representations obtained from the canonical bosonic oscillator representations over their minimal natural modules and minimal orthogonal modules by partially swapping differential operators and multiplication operators. Furthermore we construct a functor from the category of $$A_{n-1}$$ A n - 1 -modules to the category of $$A_n$$ A n -modules, which is related to n-dimensional projective transformations. Finally, we present multi-parameter families of irreducible projective oscillator representations of the algebras.

Suggested Citation

  • Xiaoping Xu, 2017. "Representations of Special Linear Algebras," Springer Books, in: Representations of Lie Algebras and Partial Differential Equations, chapter 0, pages 155-216, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6391-6_6
    DOI: 10.1007/978-981-10-6391-6_6
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