Blocks with cyclic defect of Hecke orders of Coxeter groups (Q1977795)

Let \({\mathcal H}_G\) be the Hecke order of a finite Coxeter group \(G\). For a rational prime \(p\), consider the completion \(\mathcal H\) of \({\mathcal H}_G\) at the maximal ideal \((p,q-1)\) of \({\mathcal H}_G\). If \(B\) is a block of the \(p\)-adic group ring \(\mathbb{Z}_pG\), then \(B\) lifts to a block \(\mathcal B\) of \(\mathcal H\) such that \(B\) is obtained from \(\mathcal B\) by reduction modulo \((q-1)\). The block \(\mathcal B\) is said to be of cyclic defect if \(B\) is of cyclic defect. In his main theorem the author describes a block \(\mathcal B\) of cyclic defect as a tree order over the completion of \(\mathbb{Z}[q]\) at \((p,q-1)\) [cf. \textit{K.~W.~Roggenkamp}, Colloq. Math. 82, No. 1, 25-48 (1999; Zbl 0945.16013)]. For example, if \(G\) is the symmetric group with \(p\) elements, then the Brauer tree of the principal block of \(\mathbb{Z}_pG\) is \(\mathbb{A}_p\), and the basic order of \(\mathcal B\) is the corresponding tree order. In this case, the author provides a complete list of indecomposable Cohen-Macaulay modules over \(\mathcal B\).