Poincar\'e Series for Tensor Invariants and the McKay Correspondence
Representation Theory
2015-12-17 v2
Abstract
For a finite group G and a finite-dimensional G-module V, we prove a general result on the Poincar\'e series for the G-invariants in the tensor algebra T(V). We apply this result to the finite subgroups G of the 2-by-2 special unitary matrices and their natural module V of 2-by-1 column vectors. Because these subgroups are in one-to-one correspondence with the simply laced affine Dynkin diagrams by the McKay correspondence, the Poincar\'e series obtained are the generating functions for the number of walks on the simply laced affine Dynkin diagrams.
Keywords
Cite
@article{arxiv.1407.3997,
title = {Poincar\'e Series for Tensor Invariants and the McKay Correspondence},
author = {Georgia Benkart},
journal= {arXiv preprint arXiv:1407.3997},
year = {2015}
}
Comments
Minor changes from the first edition. The paper has been accepted for publication in Advances in Mathematics