Orateur
Description
Consider the reductive dual pairs consisting of a symplectic group and an orthogonal group. The Harish-Chandra series of these two groups correspond to each other under the theta correspondence. In collaboration with Congling Qiu and Jialiang Zou, we explicitly computed this correspondence by analyzing the relevant Hecke algebra bimodules and applying a Tits deformation argument. This approach provides an alternative proof of Aubert-Michel-Rouquier's conjecture, which was initially settled by Shu-Yen Pan. In this presentation, we explore the geometrization of this construction. Consequently, we have derived a new description of the theta correspondence in terms of the Springer theory. This is a joint work with Congling Qiu, Jialiang Zou, and Zhiwei Yun.
