论文标题
有限的Coxeter组的理想型号
Perfect models for finite Coxeter groups
论文作者
论文摘要
有限组的模型是一组亚组的线性字符，可以诱导这些模型准确地获得每个不可还原字符。有限的高速公路组的理想模型是一个模型，其中相关的亚组是完美互动的准代替替代谢中心化。在先前的工作中，我们表明完美的模型引起了有趣的$ w $ graphs的有趣示例。在这里，我们对哪些有限的Coxeter组具有完美的模型进行分类。具体而言，我们证明，具有完美模型的不可约定的有限coxeter组是$ \ mathsf {a} _ {n} $，$ \ mathsf {b} _n $，$ \ mathsf {d} _ {d} _ {2n+1} $，$ \ mathsf {d} $ \ mathsf {i} _2（n）$。我们还表明，要达到自然形式的等价形式，外部类型$ \ mathsf {a} _3 $，$ \ mathsf {b} _n $和$ \ mathsf {h} _3 $，每个不可删除的有限coxeter Coxeter Group最多都有一个完美的模型。在此过程中，我们还证明了有限的代表群的表示形式的技术结果，即，至少有两个的标准抛物线亚组的诱导绝不是不含多重性的。
A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter group is a model in which the relevant subgroups are the quasiparabolic centralizers of perfect involutions. In prior work, we showed that perfect models give rise to interesting examples of $W$-graphs. Here, we classify which finite Coxeter groups have perfect models. Specifically, we prove that the irreducible finite Coxeter groups with perfect models are those of types $\mathsf{A}_{n}$, $\mathsf{B}_n$, $\mathsf{D}_{2n+1}$, $\mathsf{H}_3$, or $\mathsf{I}_2(n)$. We also show that up to a natural form of equivalence, outside types $\mathsf{A}_3$, $\mathsf{B}_n$, and $\mathsf{H}_3$, each irreducible finite Coxeter group has at most one perfect model. Along the way, we also prove a technical result about representations of finite Coxeter groups, namely, that induction from standard parabolic subgroups of corank at least two is never multiplicity-free.
