Computation of the Homology of the Complexes of Finite Verma Modules for \({K}_{4}^{\prime }\)

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 \(\mathcal {A}({K}_{4}^{\prime })\).