BASES OF INFINITE-DIMENSIONAL REPRESENTATIONS OF ORTHOSYMPLECTIC LIE SUPERALGEBRAS
Abstract
We provide explicit bases of representations of the Lie superalgebra osp(1|2n) obtained by taking tensor products of infinite-dimensional representation and the standard representation. This infinite-dimensional representation is the space of polynomials C[x₁,...,xn]. Also, we provide a new differential operator realization of osp(1|2n) in terms of differential operators of n commuting variables x₁,...,xn and 2n anti-commuting variables ξ1; : : : ; ξ2n.