Article Dans Une Revue Portugaliae Mathematica Année : 2024

A construction of the Shephard-Todd group $G_{32}$ through the Weyl group of type $E_6$

Résumé

It is well-known that the quotient of the derived subgroup of the Shephard-Todd complex reflection group $G_{32}$ (which has rank $4$) by its center is isomorphic to the derived subgroup of the Weyl group of type $E_6$. 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 $G_{32}$.

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hal-04248841 , version 1 (18-10-2023)

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Cédric Bonnafé. A construction of the Shephard-Todd group $G_{32}$ through the Weyl group of type $E_6$. Portugaliae Mathematica, 2024, 82 (1/2), pp.63-70. ⟨10.4171/PM/2119⟩. ⟨hal-04248841⟩
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