REMARKS ON METAPLECTIC TENSOR PRODUCTS FOR COVERS OF GLr

We had previously constructed a metaplectic tensor product of automorphic representations of covers of GL(r). To be precise, let M = GL(r1) x . . . x GL(rk) subset of GL(r) be a Levi subgroup of GL(r), where r = r(1) + . . . + r(k), and (M) over tilde its metaplectic preimage in the n-fold metaplectic cover (GL) over tilde (r) of GL(r). For automorphic representations pi(1), . . . , pi(k) of (GL) over tilde (r1). (A), . . . , (GL) over tilde (rk) (A), we had constructed (under certain technical assumptions, which are always satisfied when n = 2) an automorphic representation pi of (M) over tilde that can be considered as the tensor product of the representations pi(1), . . . , pi(k). Here we significantly simplify and generalize our previous construction without the technical assumptions mentioned above.