In this paper we construct an abelian category of "mixed perverse sheaves" attached to any realization of a Coxeter group, in terms of the associated Elias-Williamson diagrammatic category. This construction extends previous work of the first two authors, where we worked with parity complexes instead of diagrams, and we extend most of the properties known in this case to the general setting. As an application we prove that the split Grothendieck group of the Elias-Williamson diagrammatic category is isomorphic to the corresponding Hecke algebra, for any choice of realization.

中文翻译：

---

Coxeter 群体旗帜品种的混合反常滑轮

在本文中，我们根据相关的 Elias-Williamson 图范畴，构造了一个附加到 Coxeter 群的任何实现的“混合反常滑轮”的阿贝尔范畴。这种构造扩展了前两位作者的先前工作，在那里我们使用奇偶复数而不是图表，并且我们将这种情况下已知的大多数属性扩展到一般设置。作为一个应用，我们证明了 Elias-Williamson 图范畴的分裂 Grothendieck 群与相应的 Hecke 代数同构，对于任何实现选择。