Dade's invariant conjecture for the Chevalley groups of type G_2 in the defining characteristic

Abstract

This paper is part of a program to study the conjecture of E.C. Dade on counting characters in blocks for several finite groups. In this paper, we verify Dade's invariant conjecture for the Chevalley groups G_2(q) in the defining characteristic when q is not a power of 2 or 3. This implies Dade's final conjecture when q is not a power of 2 or 3.