Speaker: 马家骏教授，厦门大学

Inviter: 聂思安

Title: Theta Correspondence and Endo-parameters

Language: Chinese

Time & Venue: 2025.09.26 14:30-15:30 zoom：837 4395 6056 密码：123456

Abstract: The theory of semisimple characters and endo-parameters provides a powerful framework for studying smooth representations of p-adic classical groups over fields of characteristic different from p and 2 (where p ≠ 2). This theory was initiated by Bushnell, Kutzko, and Henniart for general linear groups and extended to classical groups through the work of Kurinczuk, Skodlerack, and Stevens. Endo-parameters can be viewed as restrictions of Langlands parameters to the wild inertial group, and they provide a decomposition of the category of smooth representations into subcategories that are coarser than the classical Bernstein decomposition.In this talk, I will establish a theta correspondence for semisimple characters and demonstrate that the theory of endo-parameters is compatible with theta correspondence. I will then present two applications of this result, including an explicit description of the correspondence between supercuspidal representations and a reduction-to-depth-zero theorem for theta correspondence.The talk is based on ongoing work joint with Loke, Stevens, and Trias.