Abstract
Using deformation theory, Braverman and Joseph obtained an alternative characterisation of the Joseph ideal for simple Lie algebras, which included even type A. In this note we extend that characterisation to define a remarkable quadratic ideal for \(\mathfrak {sl}(m|n)\). When \(m-n>2\), we prove that the ideal is primitive and can also be characterised similarly to the construction of the Joseph ideal by Garfinkle.
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Acknowledgements
SB is a PhD Fellow of the Research Foundation - Flanders (FWO). KC is supported by the Research Foundation - Flanders (FWO) and by Australian Research Council Discover-Project Grant DP140103239. The authors thank Jean-Philippe Michel for raising the question which led to the study in Theorem 4.
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Barbier, S., Coulembier, K. (2016). The Joseph Ideal for \(\mathfrak {sl}(m|n)\) . In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_36
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DOI: https://doi.org/10.1007/978-981-10-2636-2_36
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