Schur-Weyl Duality for Toroidal Algebras of Type $A$

Vyjayanthi Chari, Lauren Grimley, Zongzhu Lin, Chad R. Mangum, Christine Uhl, Evan Wilson

Published 2024-07-10Version 1

We state and prove an analog of the Schur-Weyl duality for a quotient of the classical $2$-toroidal Lie algebra of type $A$. We then provide a method to extend this duality to the $m$-toroidal case, $m > 2$.