Modular representations of cyclotomic algebras

本课题研究分圆Hecke代数表示理论中的前沿问题。我们的主要焦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处理这个问题，每个方向都会给出新的见解，并导致理论上的重大进步。分解数问题很重要，因为它的解给出了关于这些代数的深层结构信息，然后可以应用于其他领域。由于割圆Hecke代数在许多不同的领域有着广泛的应用，是当前数学研究的热点，因此本课题将产生很大的影响。

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.