Abstract
We compute the homology of the complexes of finite Verma modules over the annihilation superalgebra \(\mathcal {A}({K}_{4}^{\prime })\), associated with the conformal superalgebra \({K}_{4}^{\prime }\), obtained in Bagnoli and Caselli (J. Math. Phys. 63, 091701, 2022). We use the computation of the homology in order to provide an explicit realization of all the irreducible quotients of finite Verma modules over \(\mathcal {A}({K}_{4}^{\prime })\).
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Acknowledgements
This paper is based on my PhD thesis; I would like to thank my supervisors Nicoletta Cantarini and Fabrizio Caselli for their useful comments. I am also deeply grateful to Victor Kac for his precious suggestions.
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Open access funding provided by Alma Mater Studiorum - Università di Bologna within the CRUI-CARE Agreement.
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Bagnoli, L. Computation of the Homology of the Complexes of Finite Verma Modules for \({K}_{4}^{\prime }\). Algebr Represent Theor 26, 2627–2682 (2023). https://doi.org/10.1007/s10468-022-10176-9
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DOI: https://doi.org/10.1007/s10468-022-10176-9