2 problems

Let $G$ and $G'$ be a reductive dual pair, let $\widetilde{G}$ and $\widetilde{G'}$ be their corresponding covering groups, and let $\omega_{G,G'}$ be the oscillator representation…

Howe duality conjecture. The set $\mathcal R_{\omega_{U,V}}(U,V)$ is the graph of a bijection between $\mathcal R_{\omega_{U,V}}(U)$ and $\mathcal R_{\omega_{U,V}}(V)$.