Tensor product of degenerate principal series and local theta correspondence

摘要

We construct an intertwining map from the oscillator representation to the tensor product of two degenerate principal series of G and G' which form a reductive dual pair in the sense of Howe. We derive results on local theta correspondence for the dual pairs (O(p, q), Sp(2q, R)). (U(p, q), U(q, q)) and (Sp(p. q), O*(4q)), where p greater than or equal to q. We also describe the correspondence completely for the pairs (O(p, q), SL(2, R)),(U(p,q)U(1, 1)), and (Sp(p,q),O*(4)). (C) 2001 Academic Press. [References: 24]