The Demazure conjecture is a statement in the field of representation theory, specifically regarding the representation of certain algebraic groups. It was proposed by Michel Demazure in the context of the study of the characters of representations of semi-simple Lie algebras and algebraic groups. In particular, the conjecture concerns the characters of irreducible representations of semisimple Lie algebras and their relation to certain combinatorial structures associated with the Weyl group.
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