Degenerate principal series and local theta correspondence
Degenerate principal series and local theta correspondence
In this paper we determine the structure of the natural $\widetilde {U}(n,n)$ module $\Omega ^{p, q}(l)$ which is the Howe quotient corresponding to the determinant character $\det ^l$ of $U(p,q)$. We first give a description of the tempered distributions on $M_{p+q,n}(\mathbb {C})$ which transform according to the character $\det ^{-l}$ …