Semiinvariants of Finite Reflection Groups

1998/11/23 by Anne V. Shepler
Mathematics · #math.RA #math.CO #math.GR #math.GT #math.RT #msc:52B30 #msc:51F15 #msc:20H15

paper · pdf

published as J. Algebra 220, 314-326 (1999). · Paper presented at 1999 Joint Meetings in San Antonio, special session on Geometry in Dynamics. Typo corrected

arxiv created 1998/11/23 · arxiv updated 2009/11/30

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 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.

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