ON THE DIAMETERS OF MCKAY GRAPHS FOR FINITE SIMPLE GROUPS

摘要

Let G be a finite group, and alpha a nontrivial character of G. The McKay graph M(G,alpha) has the irreducible characters of G as vertices, with an edge from chi(1) to chi(2) if chi(2) is a constituent of alpha chi(1). We study the diameters of McKay graphs for simple groups G of Lie type. We show that for any alpha, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for G = PSLn(q) or PSUn(q).