Abstract
We determin the structure of the canonical bosonic and fermionic oscillator representations of type C over their minimal natural modules. Moreover, we study the noncanonical oscillator representations obtained from the above bosonic representations by partially swapping differential operators and multiplication operators. Finally, we present multi parameter families of irreducible projective oscillator representations of the algebras.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Luo, X. Xu, \(\mathbb{Z}\)-graded oscillator representations of symplectic Lie algebras. J. Algebr. 403, 401–425 (2014)
X. Xu, Projective oscillator representations of \(sl(n+1)\) and \(sp(2m+2)\). J. Lie Theory 26, 96–114 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Xu, X. (2017). Representations of Symplectic Lie Algebras. In: Representations of Lie Algebras and Partial Differential Equations. Springer, Singapore. https://doi.org/10.1007/978-981-10-6391-6_9
Download citation
DOI: https://doi.org/10.1007/978-981-10-6391-6_9
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6390-9
Online ISBN: 978-981-10-6391-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)