However Ashkenazi Levites and Sephardi Levites do not share a commonWhat might prompt you to say that?
The theory put foreward is that the AshkenaziThere cannot be - by definition - a Khazar Levite, since a person is a levite
by virtue of being a descendant of Levi, who obviously was not a Khazar. In
any case, the Khazar converts are history except in the minds of those who
would use the story to cast aspersions on the Ashkenazi Jews' heritage. This
is a particular favorite of those who would deny the Jews' connection to the
Land of Israel.