Structure of polynomial representations for orthosymplectic Lie superalgebras

Abstract

Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the structure of their various supersymmetric polynomial representations obtained by swapping bosonic multiplication operators and differential operators in the canonical supersymmetric polynomial representations. In particular, we obtain certain new infinite-dimensional irreducible representations and new composition series of indecomposable representations for these algebras.