Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425306 | Advances in Mathematics | 2016 | 24 Pages |
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)=â¨kâ¥0Vâk. We apply this result to the finite subgroups G of the 2Ã2 special unitary matrices and their natural module V of 2Ã1 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
Georgia Benkart,