Abstracto

SEMI-INVARIANTS FORMS: ABSOLUTE FINITE REFLECTION CLASS

Mukesh Kumar

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 be a multiplicative character of G. Consider the R-module of -invariant deferential forms and the R-module of -invariants in the exterior algebra of derivations. We define a natural multiplication on these modules using ideas from arrangements of hyper planes. We show that this multiplication gives each module the structure of an exterior algebra. We also define a multi-arrangement associated to , and formulate the relationship between _-invariants and logarithmic forms. We introduce a new method of computing basic derivations and the generating _-invariants and give explicit constructions for the exceptional irreducible reflection groups.