EXTENDED HIGHER-SPIN SUPERALGEBRAS AND THEIR MASSLESS REPRESENTATIONS

Three two-parameter sequences of infinite-dimensional extended higher-spin superalgebras are constructed, which give rise to consistent equations of motion of interacting gauge fields of all spins in four dimensions. In the Yang-Mills sector of spin-1 gauge fields, these higher-spin superalgebras reduce to u(n) ⊕ u(m), o(n) ⊕ o(m) and usp(n) ⊕ usp(m) with arbitrary integer parameters n ≥ 0 and m ≥ 0 (n and m are assumed to be even for symplectic algebras). Massless unitary representations of the proposed higher-spin superalgebras are analyzed. It is shown that all these superalgebras obey the admissibility condition which requires them to possess massless unitary representations with just the same spectra of spins as follows from the structure of the related higher-spin gauge fields. We argue that the infinite-dimensional (super) algebras listed in this article classify all possible higher-spin rigid (super)symmetries in four dimensions. © 1990.