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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10764 |
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Table of Contents:
- 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 $\mcal O$.