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arXiv · 2512.16095

Categorification of generic Su-Zhang character formula

Shunsuke Hirota
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Abstract

For semisimple Lie algebras, the BGG resolution is often viewed as a categorification of the Weyl character formula. For general linear Lie superalgebras, Brundan--Stroppel constructed an infinite resolution of the so-called Kostant simple modules by Kac modules, but their construction does not directly generalize the classical BGG resolution. In this paper we construct, for weights lying outside a neighborhood of the walls of the Weyl chambers, a resolution that categorifies a known Weyl-type finite-sum character formula in the same spirit as the Kac--Wakimoto formula. Our resolution is built from images of canonical homomorphisms between Verma modules attached to non-conjugate Borel subalgebras related by odd reflections. In particular, the construction developed here does generalize the classical BGG resolution.

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Shunsuke Hirota. 2025-12-18. Categorification of generic Su-Zhang character formula. https://arxiv.org/abs/2512.16095

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