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arXiv · 2604.10764

Category $\mcal O$ for polynomial toroidal algebras and its subalgebras

Priyanshu Chakraborty
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Abstract

In this paper we study Category $\mcal O$ for the polynomial toroidal Lie algebras and its $S,H$ type subalgebras. We classify irreducible objects of category $\mcal O$ as unique irreducble quotient of standard modules. Surprisingly, costandard objects of category $\mcal O$ arrises from Shen-Larsson type modules. We determine necessary sufficient conditions for irreducibility of Shen-Larsson modules. Finally appeling structure of Shen-Larsson modules and Soergel Tilting module theory of \cite{Soe}, we compute charcter formulas for irreducible modules and indecomposable Tilting modules of category $\mcal O$.

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BibTeXRIS

Priyanshu Chakraborty. 2026-04-12. Category $\mcal O$ for polynomial toroidal algebras and its subalgebras. https://arxiv.org/abs/2604.10764

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