On the Howe correspondence for symplectic–orthogonal dual pairs

We reformulate some of Moeglin’s results on the correspondence for the dual pairs (Sp(2n,R), O(p, q)) with p and q even, and fill in the cases where p and q are both odd. We arrive at a complete and detailed description, in terms of Langlands parameters, of the dual pair correspondence for the cases p + q = 2n and p + q = 2n + 2. In addition, we point out and suggest a way to correct an error in Moeglin’s paper. © 2005 Elsevier Inc. All rights reserved