Representations of Even Orthogonal Lie Algebras

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

Chapter Chapter 7 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 217-252 from Springer

Abstract: Abstract First we present the canonical bosonic and fermionic oscillator representations over their minimal natural modules of type D. Then we determine the structure of the noncanonical oscillator representations obtained from the above bosonic representations by partially swapping differential operators and multiplication operators. Furthermore, we speak about a functor from the category of $$D_n$$ D n -modules to the category of $$D_{n+1}$$ D n + 1 -modules, which is related to 2n-dimensional conformal transformations. In addition, we present multi-parameter families of irreducible conformal oscillator representations of the algebras and some of them are related to an explicitly given algebraic variety.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-6391-6_7

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DOI: 10.1007/978-981-10-6391-6_7

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