The representation theory of rational Cherednik algebras.

这个项目的目的是推进我们的理解的表示理论的理性Cherednik代数在t=0。这些代数有一个非常丰富的表示理论，但仍然知之甚少。此外，它们与可积系统、组合数学和代数几何有着密切的联系--更好地理解这种表示法将在所有这些领域都有应用。在这个项目中，我们提出了使用对称代数的理论完全分类时，（限制）的理性Cherednik代数有有限，驯服或野生表示类型。在表示类型是有限的或驯服的情况下，我们将完全分类这些代数的所有不可分解模。

The aim of this project is to advance our understanding of the representation theory of rational Cherednik algebras at t=0. These algebras have a very rich representation theory which is still poorly understood. Moreover, they have close links to integrable systems, combinatorics and algebraic geometry - a better understanding of the representation will have applications in all these areas. In this project we propose to use the theory of symmetric algebras to completely classify when the (restricted) rational Cherednik algebra has finite, tame or wild representation type. In thecases where the representation type is finite or tame, we will completely classify all indecomposable modules for these algebras.