RTG Number Theory: Theta correspondence, Hecke algebra and Springer correspondence

Abstract: In this talk, we consider the finite field theta correspondence between principle series. Joint with Jiajun Ma and Congling Qiu, we explicitly describe this correspondence by analyzing the relevant Hecke algebra bimodules and applying a deformation argument. Joint with Jiajun Ma and Congling Qiu, Zhiwei Yun, we geometrized the whole picture. Consequently, we obtained a relation between the Springer correspondence and theta correspondence.