关于$SL_n(p)$的模McKay图及其标准表示
On the modular McKay graph of $SL_n(p)$ with respect to its standard representation
摘要：
设$F$是素特征$p$的代数闭域. $G:=SL_n(p)$相对于其标准$FG$ -模$W$的模McKay图是连通的有向图，其顶点是不可约$FG$ -模，并且如果$V_2$作为张量积$V_1 \otimes W$的合成因子出现，则存在从顶点$V_1$到$V_2$的边。我们证明了这个模McKay图的直径是$\frac{1}{2} (p-1)(n^2-n)$。
英文摘要：
Let $F$ be an algebraically closed field of prime characteristic $p$. The modular McKay graph of $G:=SL_n(p)$ with respect to its standard $FG$-module $W$ is the connected, directed graph whose vertices are the irreducible $FG$-modules and for which there is an edge from a vertex $V_1$ to $V_2$ if $V_2$ occurs as a composition factor of the tensor product $V_1 \otimes W$. We show that the diameter of this modular McKay graph is $\frac{1}{2} (p-1)(n^2-n)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
