Esther 3:1

"After these events, King Xerxes honored Haman son of Hammedatha, the Agagite, elevating him and giving him a seat of honor higher than that of all the other nobles." NIV translation

After the plot to kill the king was dealt with, he honored Haman to a position higher than anyone else. This man was an Agagite which means he was descended from the royal family of the Amalekites. This is the same group of people that attacked God's people when they were on their way to the promised land from Egypt and they became known for their cowardice and cruelty (see Exodus 17:8-16). 

They were descended from the grandson of Esau which was Jacob's twin brother and Jacob was the father of the tribes of Israel.

We can see by this that the cause of antisemitism is a simple case of jealousy between brothers. It is no different than the story of Cain's jealousy and murder of Abel (Genesis 4). According to traditional Arab history, the Amalekites originated from the area of Mecca in what is known today as Saudi Arabia.

Esther 3:2

"All the royal officials at the king's gate knelt down and paid honor to Haman, for the king had commanded this concerning him. But Mordecai would not kneel down or pay him honor." NIV translation

So the king ordered everyone to bow down to Haman but Mordecai would not. We must remember that Mordecai was a Jew and it was against the Mosaic Law to bow down to anyone but God. ( We can see another example of this in Daniel chapter three.)