Harmonic analysis over Chevalley groups and number theory

This PhD project will be aiming at generalizing Deligne-Lustig theory and Springer correspondence to arbitrary Chevalley groups. The project may start with extending these theories to some classical groups such as symplectic groups and orthogonal groups. The Hecke algebras defined on general linear groups over arbitrary fields will also be studied. The study of representations of Chevalley groups has many applications to number theory, such as automorphic forms and p-adic analysis. It also helps to seek the some interplays among symmetric groups, general linear groups over local fields and finte fields, which may finally linked to Langlands correspondence