BGV’s homomorphic rotation scheme of input vector slots is exactly the same as BFV’s rotation scheme (Summary D-2.9 in §D-2.9).
Summary D-4.10 BGV’s Homomorphic Rotation of Input Vector Slots
Suppose we have a BGV ciphertext and a key-switching key as follows:
Then, the procedure of rotating the first-half elements of the ciphertext’s original input vector by positions to the left (in a wrapping manner among them) and the second-half elements of by positions to the left (in a wrapping manner among them) is as follows: