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-d imensional complex Lie superalgebra. This character formula had been c onjectured earlier by Vera Serganova and the author for any generic ir reducible finite-dimensional g-module, i.e. such that its highest weig ht 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 g is isomorphic to psq(n) for n greater than or equal to 3 or to H(2k + 1) for k greater than or equal to 2, strong genericity is equivalent to genericity.