Analogs of Bol operators on superstrings

Abstract

The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the [Formula: see text]-dimensional supermanifold (superstring) [Formula: see text], we classify analogs of Bol operators invariant under the simple maximal subalgebra [Formula: see text] of the same rank as its simple ambient superalgebra [Formula: see text] of vector fields on [Formula: see text] and containing all elements of negative degree of [Formula: see text] in a [Formula: see text]-grading. We also consider the Lie superalgebras of vector fields [Formula: see text] preserving a contact structure on the superstring [Formula: see text]. We have discovered many new operators.