The Fock wave function as classified by the supergroup chain U(N/M)⊃OSp(N/M)⊃O(N)×Sp(M)

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Abstract
The wave functions for bosons and fermions, classified according to the supergroup chain U(N/M)⊃OSp(N/M)⊃O(N)×Sp(M)⊃⋅ ⋅ ⋅, are given in this paper. The method presented here adheres closely to the standard raising and lowering method commonly used in quantum mechanics. When the so‐called star representation [n} is decomposed into the irreducible representation of the OSp(N/M), one obtains a reducible, but not completely reducible, representation of the OSp(N/M). This decomposition is quite different from a regular Lie group chain and has very interesting physical implications.