The Kazhdan-Lusztig Conjecture is a significant hypothesis in representation theory and algebraic geometry that connects the characters of irreducible representations of a semisimple Lie algebra with the combinatorial structures of its associated Weyl group. It provides a deep relationship between the geometry of the flag variety and the representation theory of the associated Lie algebra, particularly through the use of a specific formula involving Kazhdan-Lusztig polynomials.
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