Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weyl-Kac character formula for affine Lie algebra in Deligne's category   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 Weyl-Kac formula to compute the character of the irreducible quotient
$L(X,k)$ of the parabolic Verma module $M(X,k)$ of level $k$, where $X$ is an
indecomposable object of Deligne's category $\underline{\mathrm{Rep}}(GL_t)$,
$\underline{\mathrm{Rep}}(O_t)$, or $\underline{\mathrm{Rep}}(Sp_t)$, under
conditions that the highest weight of $X$ plus the level gives a fundamental
weight, $t$ is transcendental, and the base field $\Bbbk$ has characteristic
$0$. We compare our result to the partial result of Etingof, and evaluate the
characters to the categorical dimensions to get a categorical interpretation of
the Nekrasov-Okounkov hook length formula.

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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin