Analogue of Kostant's u-cohomology formula for the general linear superalgebra

Abstract

We determine in an explicit form the Lie superalgebra cohomology groups of the upper triangular odd subalgebra (Glm|n)+1 of the general linear superalgebra Glm|n with coefficients in irreducible tensor modules over Glm|n. Using this, we develop a Weyl-type character formula for the irreducible tensor representations. Both in the computation of the cohomology groups and in the construction of the character formula, the Weyl group of the infinite-rank affine Kac-Moody algebra of A-type plays an essential role.