The Local Theta Correspondence

Progressing from foundational material to the latest developments, this text provides a definitive treatment of the local theta correspondence over p-adic fields. Bringing together material currently spread throughout the literature, it delves into topics such as the Weil representation, the Heisenberg group, metaplectic groups, Leray cocycles, and more. It features complete proofs of important recent results, notably including the first complete exposition of the Howe duality conjecture and the conservation relations for first occurrence indices in towers. With a careful and accessible discussion of background material, this book enables students to get to grips with this fascinating area, while its in-depth coverage renders it an ideal reference for researchers working in representation theory of p-adic groups and automorphic representations.