论文信息 - Institute for Mathematical Physics Generic Irreducible Representations of Finite-dimensional Lie Superalgebras Generic Irreducible Representations of Finite-dimensional Lie Superalgebras

Institute for Mathematical Physics Generic Irreducible Representations of Finite-dimensional Lie Superalgebras Generic Irreducible Representations of Finite-dimensional Lie Superalgebras

A theory of highest weight modules over an arbitrary finite-dimensional Lie superalgebra is constructed. A necessary and sufficient condition for the finite-dimensionality of such modules is proved. Generic finite-dimensional irreducible representations are defined and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic finite-dimensional irreducible module over any finite-dimensional Lie superalgebra. The conjecture is proved for several classes of Lie superalgebras, in particular for all solvable ones, for all simple ones, and for certain semi-simple ones.

Vera Serganova | Ivan Penkov | V. Serganova | I. Penkov

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