论文标题
阶乘多参数hecke von neumann代数和作用于右角建筑物的群体的代表
Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings
论文作者
论文摘要
我们获得了与右角共同组相关的阶乘多参数hecke von neumann代数的完整表征。考虑到他们的$ \ ell^p $ - 卷积代数类似物，我们表现出有趣的参数依赖性，对比班克代数较早观察到的对比现象。这些结果翻译成Iwahori-Hecke von Neumann代数，使我们能够对作用于右角建筑物的群体的球形代表理论得出结论，这些理论与仿射情况下的球形表示行为形成了鲜明的对比。我们还研究了右角Coxeter组的某些图形产品表示形式，并注意到我们的von Neumann代数结构结果表明，这些是有限因子表示。进一步将合适的家族分类为统一等效性，使我们能够揭示右角coxeter群体极端特征空间的高维欧几里得子空间。
We obtain a complete characterisation of factorial multiparameter Hecke von Neumann algebras associated with right-angled Coxeter groups. Considering their $\ell^p$-convolution algebra analogues, we exhibit an interesting parameter dependence, contrasting phenomena observed earlier for group Banach algebras. Translated to Iwahori-Hecke von Neumann algebras, these results allow us to draw conclusions on spherical representation theory of groups acting on right-angled buildings, which are in strong contrast to behaviour of spherical representations in the affine case. We also investigate certain graph product representations of right-angled Coxeter groups and note that our von Neumann algebraic structure results show that these are finite factor representations. Further classifying a suitable family of them up to unitary equivalence allows us to reveal high-dimensional Euclidean subspaces of the space of extremal characters of right-angled Coxeter groups.
