Abstract
In 1979, Bernstein, Gelfand, and Gelfand described a duality between certain parts of the derived categories of the symmetric and exterior algebras. This type of duality, called Koszul duality, has since been observed in various contexts. After introducing the necessary homological algebra, we formulate this phenomenon as a differential graded version of Morita theory, and present Koszul duality for a polynomial ring in one variable. We then present some evidence (on the level of characters) of such a self-duality in the principal block of category \(\mathcal {O}\).
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