Abstract

We study the characters of simple modules in the parabolic BGG category of the affine Lie algebra in Deligne's category. More specifically, we take the limit of the Weyl-Kac formula to compute the character of the irreducible quotient of the parabolic Verma module with the dominant highest weight in a Deligne's category with t transcendental, and the base field of characteristic 0. We compare our result to the partial result in Etingof's paper, and evaluate the characters to the categorical dimensions to get a categorical interpretation of the Nekrasov-Okounkov hook length formula.--Author's abstract

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