REPRESENTATIONS OF CLASSICAL LIE-SUPERALGEBRAS OF TYPE-I

An explicit description of a generic irreducible module (possibly infinite dimensional and not necessarily diagonalizable over some Cartan subsuperalgebra) over a finite dimensional classical Lie superalgebra G of type I is given in terms of its irreducible G0-submodules. For a finite dimensional module the result reduces to a character formula, proved earlier by J. Bernstein and D. Leites for the Lie superalgebras gl(1 + mepsilon), gl(m + epsilon), osp(2 + nepsilon). In the finite dimensional case a character formula for another class, of so-called relatively typical, irreducible modules is also proved and illustrated by explicit examples.