Nonstandard matrix formats of lie superalgebras

The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we present a systematic study of other possible matrix formats and in particular of the so-called diagonal format which naturally occurs in various physical applications, e.g. for the supersymmetric versions of conformal field theory, integrable models. W algebras and quantum groups.