Elsevier

Journal of Algebra

Volume 220, Issue 1, 1 October 1999, Pages 314-326
Journal of Algebra

Regular Article
Semi-invariants of Finite Reflection Groups

https://doi.org/10.1006/jabr.1999.7875Get rights and content
Under an Elsevier user license
open archive

Abstract

Let G be a finite group of complex n × n unitary matrices generated by reflections acting on Cn. Let R be the ring of invariant polynomials, and let χ be a multiplicative character of G. Let Ωχ be the R-module of χ-invariant differential forms. We define a multiplication in Ωχ and show that under this multiplication Ωχ has an exterior algebra structure. We also show how to extend the results to vector fields, and exhibit a relationship between χ-invariant forms and logarithmic forms.

Cited by (0)

Communicated by Georgia, Benkart

f1

[email protected]