【摘要】 <正>K表示特征数p>0的代数闭域。G是K上单连通半单代数群。Γ_n=G（FPⁿ）是Pⁿ个元素的有限域上型G的有限Chevalley群,它在K上的群代数是KΓ_n.Λ_n表示不同构的不可约KΓ_n-模M_λ,n的指标集,也是不同构的主不可分解KΓ_n-模R_λ,n的指标集,它可以看作G的权格X中“限制”优势权的集合X_pⁿ。因此|Λ_n|=p⁽R·rankG.Γ_n的Cartan不变量C₍λ,μ（λ,μ∈Λ_n）等于M_μ,n作为R_λ,n的合成因子出现的重数,形成|Λ_n|阶对称矩阵。更多还原

【Abstract】 Let G = SL(3,K) be a simply connected, semi-simple algebraic group of type A2 over an algebraically closed i’ield K of characteristic p>0. Let Γn = SL(3,pn) be a finite subgroup consisting of fixed points oi’ the Frobenius morphism Fn of G.In this paper, a method for computing the Cartan invariants of Γn for p>3 is. given and the Cartan matrix of SL(3,7) is computed. We mainly deal with Γ1 and find the KΓ1- compos it ion factors of each principal indecomposable KΓ1-module- by the following way: It is known that the principal indecomposable μ1-module Qλ.1 has a G-module structure, we first prove that it has a G-module filtration with quotients isomorphic to Weyl modules and give a general description of its quotients (§　1.4. Theorems). Next we write general expressions of decomposition of Qλ.1 into G-composition factors and μ1-composition factors (§4.5. Theorem 10 and Theorem 11). Using deformation we obtain all KΓ1-composition factors of Qλ1(§1.6.). Since the restriction of Qλ.1 to KΓ1is still projective, it can be written as a direct sum principal indecomposable KΓ1-modules, we thus obtain all KΓ1-composition factors of Rλ.1 We further show how to generalize our method to compute the KΓn-composition factors of Rλn for all and describe the behaviours of KΓn-compositi6n factors of Rλ.n when λ is in a general position in An (§3.).更多还原