Article ID Journal Published Year Pages File Type
6425306 Advances in Mathematics 2016 24 Pages PDF
Abstract
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 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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
Authors
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