Modular representations of cyclotomic algebras

这个项目解决了割圆Hecke代数的表示理论中的前沿问题。我们的主要重点将是计算这些代数的分解矩阵。我们从几个不同的方向来探讨这个问题，每个方向都将提供新的见解，并导致理论的重大进展。分解数问题是重要的，因为它的解决方案提供了这些代数的深层结构信息，然后可以应用于其他领域。由于分圆Hecke代数在许多不同的领域都有应用，并且它们是当前数学研究的热点，因此该项目将具有很高的影响力。

This project addresses cutting edge questions in the representation theory of cyclotomic Hecke algebras. Our main focus will be computing decomposition matrices for these algebras. We approach this question from several different directions, each of which will give new insights and lead to significant advances in the theory. The decomposition number problem is important because its' solution gives deep structural information about these algebras which can then be applied in other areas. This project will have high impact because cyclotomic Hecke algebras have applications in many different areas and they are currently a hot topic of research in mathematics.