draw a character sketch of the emperor of lilliput
Answers
By sketch, I am assuming you mean a literary sketch of the Lilliputian emperor. As you know, the Lilliputians are physically tiny people, and Swift plays upon their physical size by linking that to their "smallness" in character.
The emperor of Lilliput is egocentric and acts much like a despotic ruler. He demands that his officials walk on tightropes and perform other dangerous acts to obtain and keep their jobs. They oblige, even though these feats have nothing to do with their jobs, just to keep the emperor happy.
The leader also shows a lack of judgment in allowing a fight between two nations to rage on about the proper method to crack eggs. This long, insignificant battle has raged for years and cost many lives.
In order to be freed from his bonds, Gulliver must agree to a long list of items, including defending Lilliput at all costs. However, the emporer shows his lack of appreciation for Gulliver both saving his wife's life in the burning castle and for repelling an attack on Lilliput by impeaching him.
Gulliver eventually is freed from his stay with the small-minded Lilliputians and goes on to bigger and better places.