A construction of the Shephard–Todd group through the Weyl group of type
Cédric Bonnafé
Université de Montpellier, France
![A construction of the Shephard–Todd group $G_{32}$ through the Weyl group of type $\mathrm{E_6}$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-pm.png&w=3840&q=90)
Abstract
It is well known that the quotient of the derived subgroup of the Shephard–Todd complex reflection group (which has rank ) by its center is isomorphic to the derived subgroup of the Weyl group of type . We show that this isomorphism can be realized through the second exterior power, and take the opportunity to propose an alternative construction of the group .
Cite this article
Cédric Bonnafé, A construction of the Shephard–Todd group through the Weyl group of type . Port. Math. (2024), published online first
DOI 10.4171/PM/2119