u-Cohomology formula for unitarizable modules over general linear superalgebras

The u-cohomology groups with coefficients in infinite-dimensional irreducible unitarizable highest weight modules are introduced for the general linear superalgebra. The corresponding cohomology groups associated with a large class of infinite-dimensional irreducible unitarizable representations known as the oscillator representations are computed explicitly. Results lead to a more detailed understanding of the character formula for such modules derived in an earlier publication using other methods.