This article addresses the question of whether Langlands duality for complex reductive Lie groups may be implemented by T-dualization. We prove that for reductive groups whose simple factors are of Dynkin type A, D, or E, the answer is yes.
"T-duality for Langlands dual groups." Adv. Theor. Math. Phys. 18 (6) 1267 - 1285, December 2014.