question on ventilation in open kitchen

Hi all. I've recently renovated my one-bedroom coop in Brooklyn and opened the previously very small closed off-kitchen so that it is open to the living room, separated only by a kitchen island. The living room has many large windows. The vent in the previous kitchen configuration has been covered by a cabinet, and the building management is now insisting that I install a new vent. Now that the kitchen is open to the living room, can the living room windows not be considered adequate ventilation for the small kitchen, too? Does anyone know what the code is on this? Thanks!