Image of transfer from GL(2) × GL(3) to GL(6) done with latex

We characterize the image of the functorial transfer from GL(2) × GL(3) to GL(6) over global fields in cyclic automorphic induction cases by using available automorphic tools. Over local fields we characterize the image in general. We also characterize the transfer image from GL(2) × GL(2) to GL(4). We find a representation of SL(4, [special characters omitted]) for which the tensor subgroup SL(2, [special characters omitted]) ⊗ SL(2, [special characters omitted]) is a stabilizer subgroup. We also find a representation of SL(6, [special characters omitted]) for which the tensor subgroup SL(2, [special characters omitted]) ⊗ SL(3, [special characters omitted]) is the identity component of a stabilizer subgroup. These representations are crucial to the characterization of the image of the corresponding transfer in general based on Langlands' philosophy