On the Howe correspondence for symplectic–orthogonal dual pairs

AbstractWe 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