The sign representation for shephard groups

Peter Orlik, Victor Reiner, Anne V. Shepler

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Shephard groups are unitary reflection groups arising as the symmetries of regular complex polytopes. For a Shephard group, we identify the representation carried by the principal ideal in the coinvariant algebra generated by the image of the product of all linear forms defining reflecting hyperplanes. This representation turns out to have many equivalent guises making it analogous to the sign representation of a finite Coxeter group. One of these guises is (up to a twist) the cohomology of the Milnor fiber for the isolated singularity at 0 in the hypersurface defined by any homogeneous invariant of minimal degree.

Original languageEnglish (US)
Pages (from-to)477-492
Number of pages16
JournalMathematische Annalen
Issue number3
StatePublished - 2002


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