GENERIC IRREDUCIBLE REPRESENTATIONS OFFINITE - DIMENSIONAL LIE SUPERALGEBRASIvan
نویسنده
چکیده
A theory of highest weight modules over an arbitrary nite-dimensional Lie su-peralgebra is constructed. A necessary and suucient condition for the nite-dimensionality of such modules is proved. Generic nite-dimensional irreducible representations are deened and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic nite-dimensional irreducible module over any nite-dimensional Lie superalgebra. The conjecture is proved for several classes of Lie su-peralgebras, in particular for all solvable ones, for all non-exceptional simple ones, and for certain semi-simple ones.
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