Semiinvariants of Finite Reflection Groups
Rings and Algebras
2007-05-23 v2 Combinatorics
Group Theory
Geometric Topology
Representation Theory
Abstract
Let G be a finite group of complex n by n unitary matrices generated by reflections acting on C^n. Let R be the ring of invariant polynomials, and \chi be a multiplicative character of G. Let \Omega^\chi be the R-module of \chi-invariant differential forms. We define a multiplication in \Omega^\chi and show that under this multiplication \Omega^\chi has an exterior algebra structure. We also show how to extend the results to vector fields, and exhibit a relationship between \chi-invariant forms and logarithmic forms.
Cite
@article{arxiv.math/9811051,
title = {Semiinvariants of Finite Reflection Groups},
author = {Anne V. Shepler},
journal= {arXiv preprint arXiv:math/9811051},
year = {2007}
}
Comments
Paper presented at 1999 Joint Meetings in San Antonio, special session on Geometry in Dynamics. Typo corrected