Abstract
We study finite W-algebras corresponding to the regular nilpotent orbits for classical Lie superalgebras of Type I. In the case when the Lie superalgebra has defect 1 we give a complete description of the finite W-algebras. We also present some partial results for the case \(\mathfrak{g}\mathfrak{l}(n\vert n)\) and formulate a general conjecture about the structure of these algebras.
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Acknowledgements
The authors would like to thank the Mathematisches Forschungsinstitut Oberwolfach for the hospitality and support in the spring of 2010. They also thank Crystal Hoyt for stimulating discussions and pointing out [1] and [3].
E.P. thanks the organizers of the 9-th International Workshop “Lie Theory and Its Applications in Physics” (LT-9), 20–26 June 2011, Varna, Bulgaria, for the very interesting conference and for the hospitality.
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Poletaeva, E., Serganova, V. (2013). On Finite W-Algebras for Lie Superalgebras in the Regular Case. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_36
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DOI: https://doi.org/10.1007/978-4-431-54270-4_36
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