Characters of Strongly Generic Irreducible Lie Superalgebra Representations

An explicit character formula is established for any strongly generic finite-dimensional irreducible g-module, g 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 g-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 then genericity, but if in particular no simple component of g is isomorphic to psq(n) for n ≥ 3 or to H(2k + 1) for k ≥ 2, strong genericity is equivalent to genericity.