A Noncrossing Basis for Noncommutative Invariants of SL(2,C)
Combinatorics
2012-12-06 v1
Abstract
Noncommutative invariant theory is a generalization of the classical invariant theory of the action of on binary forms. The dimensions of the spaces of invariant noncommutative polynomials coincide with the numbers of certain noncrossing partitions. We give an elementary combinatorial explanation of this fact by constructing a noncrossing basis of the homogeneous components. Using the theory free stochastic measures this provides a combinatorial proof of the Molien-Weyl formula in this setting.
Keywords
Cite
@article{arxiv.0905.1860,
title = {A Noncrossing Basis for Noncommutative Invariants of SL(2,C)},
author = {Franz Lehner},
journal= {arXiv preprint arXiv:0905.1860},
year = {2012}
}
Comments
AMS LaTeX, 13 pages, using Asymptote pictures