The First Cartan Invariant of SL(3, 3n) and SU(3,3n)

摘要

The determination of Cartan invariants is an important aspect in the modular representations of algebraic groups and related finite groups of L.ie type. In this paper, the first Cartan invariants for the groups SL(3,3") and SU(3,3") are calculated by using some results from the representations of algebraic groups. Our main results are as follows:where a,b are the roots of the polynomial x~2-20x+48.