Abstract
Motivated from understanding higher-dimensional supersymmetric conformal field theory, we study various inhomogeneous oscillator representations of and on supersymmetric polynomial algebras and on spaces of supersymmetric exponential–polynomial functions, analogous to the projective oscillator representations of and . In particular, we find the explicit structures of certain Harish-Chandra modules and Whittaker-type modules of these Lie superalgebras.
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