文摘
For a finite group G and a finite-dimensional G-module V, we prove a general result on the Poincaré series for the G-invariants in the tensor algebra T(V)=⨁k≥0V⊗k. We apply this result to the finite subgroups G of the c993167b290d9b7ef6f28607b8b56a" title="Click to view the MathML source">2×2 special unitary matrices and their natural module V of 2×1 column vectors. Because these subgroups are in one-to-one correspondence with the simply laced affine Dynkin diagrams by the McKay correspondence, the Poincaré series obtained are the generating functions for the number of walks on the simply laced affine Dynkin diagrams.