I don’t know what law would prohibit this. Nor do I think it is an issue of separation of church and state. It is a question of appropriateness, however.
If there were Hindu members of the Senate, then it would be appropriate from a pastoral sense. If there is not a member being represented in the Senate, then there would be no point in having a Hindu pray because, as I understand it, this is a prayer for the Senators. I personally don’t see any problem with representatives of a religion, practiced by the members, praying.
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