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Published in:
2017 | OriginalPaper | Chapter
7. Representations of Even Orthogonal Lie Algebras
Author : Xiaoping Xu
Published in: Representations of Lie Algebras and Partial Differential Equations
Publisher: Springer Singapore
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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 \(D_n\)-modules to the category of \(D_{n+1}\)-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.