Some integral representations of complex reflection groups (Q1868748)

Let \(G\) be a finite unitary group generated by complex reflections. The group \(G\) consists of matrices generated by complex reflections. Let \(F\) be a field containing \(\mathbb{Q}(G)\). Let \(R\) be the ring of integers in \(F\). Then \(G\) can be written as a group of matrices with entries in \(R\). Such a representation of \(G\) is called a reflection representation of \(G\). Let \(N(G,F)\) denote the number of \(R\)-equivalence classes of \(R\)-representations of \(G\) which are \(F\)-equivalent to a reflection representation. Let \(N(G)=N(G,\mathbb{Q}(G))\). The paper is devoted to the calculation of \(N(G)\) for all types of finite unitary groups generated by complex reflections.