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Explore a detailed mathematics seminar talk that delves into the representation theory of affine Lie algebras, focusing on critical level representations. Learn about the block decomposition of category O through the Harish-Chandra homomorphism in the finite dimensional case, before advancing to infinite dimensional generalizations using the Segal-Sugawara operator. Discover the proof of center triviality for generic levels and gain insights into the center description at critical level through vertex operator algebras. Delivered by Elchanan Nafcha in 2023, this 103-minute presentation provides a comprehensive overview of affine Lie algebra representation theory with particular emphasis on fixed level representations.
