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

Abstract

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, $m>2$.

References in corpus (3)

• Schur duality in the toroidal setting
• Fermionic realization of toroidal Lie algebras of classical types
• Schur--Weyl duality over commutative rings