Local theta correspondences between epipelagic supercuspidal representations (Q284788)

Let \((G, G')\) be an irreducible reductive dual pair of type I, defined over a \(p\)-adic field with \(p\neq 2\). The main result of the paper, Theorem 8.1.2, asserts that, besides an exceptional case, two epipelagic supercuspidal representations \(\pi\) of \(\widetilde G\) (the double cover of \(G\) induced by the metaplectic cover) and \(\pi'\) of \(\widetilde G'\) are related by the Howe correspondence if and only if the epipelagic data of \(\pi\) and \(\pi'\) are related by the moment map.