Semiinvariants of Finite Reflection Groups
Abstract
Description
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 χbe a multiplicative character of G. Let Ω^χbe the R-module of χ-invariant differential forms. We define a multiplication in Ω^χand show that under this multiplication Ω^χhas 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.
Paper presented at 1999 Joint Meetings in San Antonio, special session on Geometry in Dynamics. Typo corrected
Paper presented at 1999 Joint Meetings in San Antonio, special session on Geometry in Dynamics. Typo corrected