Discrete complex reflection groups (Q6588459)

This paper is a retelling of the readings the author gave in 1983 at the University of Utrecht [Discrete complex reflection groups. Utrecht: Mathematisch Instituut der Rijksuniversiteit Utrecht (1982; Zbl 0481.20030)]. Their subject matter is the author's classification of discrete groups generated by complex reflections of Hermitian affine spaces \(\mathbb{C}^{n}\) (named here \(r\)-groups). The goal of lectures was to present the results of classification, along with the main ideas, statements and proofs that make it possible to obtain these results.\N\NThe paper is divided into five paragraphs: (I) Notation and formulation of the problem. (II) Formulation of the results. (III) Several auxiliary results and the classification of infinite complex irreducible noncrystallographic \(r\)-groups. (IV) Invariant lattices (here the properties of the operator \(S\) are introduced). (V) The structure of \(r\)-groups in the case \(s=n+1\).