be under the illusion that

believe mistakenly that

錯誤地認為

the world is under the illusion that the original painting still hangs in the Winter Palace.

全世界的人都錯誤地認為原畫還掛在冬宮內。

be under no illusion (或 illusions)

be fully aware of the true state of affairs

對真實事態一清二楚