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.

KEYWORDS:

• Multiloop Lie algebras
• Schur-Weyl duality
• toroidal Lie algebras

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B67
• 17B65
• 20G43

Acknowledgments

The project was made possible by a SQuaRE at the American Institute of Mathematics. The authors thank AIM for providing a supportive and mathematically rich environment.

Additional information

Funding

VC also acknowledges support from the Infosys Visiting Chair position at IISc.