Representations of the exceptional Lie superalgebra E(3,6) III: Classification of singular vectors

Abstract

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3,6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sl(3)\times sl(2)\times gl(1) as the zero degree component of its consistent ZZ-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3,6), completing thereby the classification and construction of all irreducible E(3,6)- modules that are L_0-locally finite.