The character table of a finite group G contains the relevant information to classify linear actions of G on vector spaces. Orthogonal character tables additionally allow to read off the relevant information about the G-invariant quadratic, Hermitian or symplectic forms. The project aims to determine the generic orthogonal character tables for finite groups of Lie type. Standard tools include restriction to parabolic subgroups and the action of the corresponding Iwahori-Hecke algebra.
