Abstract
By using the idea of Wakimoto’s free field, we construct a class of representations for the Lie superalgebra D(2, 1; α) on the tensor product of a polynomial algebra and an exterior algebra involving one parameter λ. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact, the representation is irreducible if and only if the parameter λ satisfies \((\lambda + m)(\lambda - \frac{1+\alpha}{\alpha}m) \neq 0\) for any m ∈ ℤ+.
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Acknowledgements
We thank Dr. Yong Jie Wang for some useful discussion. We thank the referees for their time and comments.
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Supported by NSF of China (Grant Nos. 11701340 and 11271043)
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Cheng, J., Zeng, Z.T. Irreducible Wakimoto-like Modules for the Lie Superalgebra D(2, 1;α). Acta. Math. Sin.-English Ser. 34, 1578–1588 (2018). https://doi.org/10.1007/s10114-018-7265-9
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DOI: https://doi.org/10.1007/s10114-018-7265-9