论文标题
等级的本地theta对应关系是强大的莫里塔等效性
Equal rank local theta correspondence as a strong Morita equivalence
论文作者
论文摘要
让（G，h）在特征零的非架构本地字段上，是等级还原双对（MP_ {2N}，O_ {2n+1}）或（u_n，u_n）。众所周知，theta对应关系在某些子集（例如r（g）和r（h）之间建立了两次射击的b和r（r（h））。这种等效性是由与莫里塔等价双模块相关的感应函子（在rieffel的意义上）实现的，我们使用振荡器表示构建。作为直接的推论，我们推断出双眼在弱包容方面起作用且连续。我们在角色转移和保留正式学位方面产生了进一步的后果。
Let (G,H) be one of the equal rank reductive dual pairs (Mp_{2n},O_{2n+1}) or (U_n,U_n) over a non-archimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain subsets, say R(G) and R(H), of the tempered duals of G and H. We prove that this bijection arises from an equivalence between the categories of representations of two C*-algebras whose spectra are R(G) and R(H). This equivalence is implemented by the induction functor associated to a Morita equivalence bimodule (in the sense of Rieffel) which we construct using the oscillator representation. As an immediate corollary, we deduce that the bijection is functorial and continuous with respect to weak inclusion. We derive further consequences regarding the transfer of characters and preservation of formal degrees.
