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