Commutative operators for double Yangian \(DY(sl_n)\)

Sa？etak We derive explicit formulae for certain commutative vertex operators associated with Iohara's realization of the level 1 \(DY(sl_n)\)-modules. As an application, we construct combinatorial bases for the corresponding principal subspaces and recover the classical character formulae. In the end, we discuss the underlying nonlocal vertex algebra theory