An explicit character formula is established for any strongly generic finite-dimensional irreducible [Formula: see text]-module, [Formula: see text] being an arbitrary finite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible finite-dimensional [Formula: see text]-module, i.e. such that its highest weight is far enough from the walls of the Weyl chambers. The condition of strong genericity, under which the conjecture is proved in this paper, is slightly stronger than genericity, but if in particular no simple component of [Formula: see text] is isomorphic to psq(n) for n ≥ 3 or to H(2k + 1) for k ≥ 2, strong genericity is equivalent to genericity.
The Kac–Wakimoto character formula for the general linear Lie superalgebra
