All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Neither the Imam nor the Muslims who are praying with him should raise their hands during the Khutbah (Friday sermon) except during the Istisqaa’ prayer (i.e. the prayer for rain). In this case, it is even a Sunnah for them to do so. On the other hand, the scholars have divided raising hands when making Du'aa’ (supplication) into three situations.
First, if it is proved that the Prophet raised his hands during a given supplication, in this case it is a Sunnah to do so like during the Istisqaa’ supplication.
Second, if it is proved that the Prophet made a certain Du'aa’ and did not raise his hands, like his Du'aa’ during Friday Khutbah except while making Istisqaa’, and his Du'aa’ between the two prostrations and before the Tasleem (i.e. saying Assalaamu Alaykum to conclude the prayer); it is not recommended by the Sharee’ah to raise hands during these situations because the Prophet's deed is an evidence to do something, and his avoidance from doing something is also a proof that that thing is not to be done.
The third situation is all types of Du'aa’ which do not fit into one of the above categories. In this case it is from the Sharee’ah that the person raises his hands for the Ahadeeth that urge doing so and which state that raising the hands in Du'aa’ is a cause for having ones Du'aa’ answered.
The Prophet said: “Your Lord is munificent and generous, and is ashamed to turn away empty the hands of His Servant when he raises them to Him.” [Abu Daawood and At-Tirmithi]
Allah knows best.