Matrix factorisations arising from well-generated complex reflection groups

EL-Shellability of Generalized Noncrossing Partitions Associated to Well-Generated Complex Reflection Groups

In this article we prove that the poset of m-divisible noncrossing partitions is EL-shellable for every wellgenerated complex reflection group. This was an open problem for type G(d, d, n) and for the exceptional types, for which a proof is given case-by-case. Résumé. Dans cet article nous prouvons que l’ensemble ordonné des partitions non-croisées m-divisibles est ELépluchable (“EL-shellable”)...

Self-products of Elliptic Curves Arising from Reflection Groups

We prove that quotients of complex vector spaces by lattices of maximal rank invariant with respect to irreducible (complex) reflection groups are isogenous to self-products of elliptic curves, and that for reflections groups which are not the complexifications of the Weyl groups of irreducible root systems, they are isomorphic to self-products of mutually isogenous elliptic curves with complex...

Automorphisms of complex reflection groups

I. MARIN AND J. MICHEL Abstract. Let G ⊂ GL(Cr) be an irreducible finite complex reflection group. We show that (apart from the exception G = S6) any automorphism of G is the product of an automorphism induced by tensoring by a linear character, of an automorphism induced by an element of NGL(Cr)(G) and of what we call a “Galois” automorphism: we show that Gal(K/Q), where K is the field of defi...

Unitriangular factorisations of Chevalley groups

Fusion Algebras for Imprimitive Complex Reflection Groups

We prove that the Fourier matrices for the imprimitive complex reflection groups introduced by Malle in [9] define fusion algebras with not necessarily positive but integer structure constants. Hence they define Z-algebras. As a result, we obtain that all known Fourier matrices belonging to spetses define algebras with integer structure constants.