Irreducible modules in category O for polynomial toroidal algebras are unique quotients of standard modules, with character formulas derived from Shen-Larsson modules and Soergel tilting theory.
Rudakov,Irreducible representations of infinte-dimensional Lie algebras of Cartan type
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Category $\mcal O$ for polynomial toroidal algebras and its subalgebras
Irreducible modules in category O for polynomial toroidal algebras are unique quotients of standard modules, with character formulas derived from Shen-Larsson modules and Soergel tilting theory.