任意Weyl群的分圆非退化Hecke代数
The cyclotomic non-degenerate Hecke algebras of arbitrary Weyl groups
AI总结：
该研究为任意Weyl群的非退化仿射Hecke代数构造KLR型生成元，建立了分圆Hecke代数块直和与KLR型代数分圆商的同构，明确了两类模分解的对应关系。
AI中文摘要：
我们为与任意Weyl群相关的某些非退化仿射Hecke代数的修正形式在局部化后构造了类似Khovanov–Lauda–Rouquier（KLR）的生成元，这些生成元给出了修正代数的非分次KLR型表示。作为应用，我们建立了任意Weyl群的分圆Hecke代数的块直和与所得非分次KLR型代数的分圆商之间的同构，还解释了这些同构如何将分圆Hecke模的广义权空间分解与KLR型表示的模的幂等分解对应起来。
英文摘要：
We construct Khovanov--Lauda--Rouquier-like generators for certain modified forms of non-degenerate affine Hecke algebras associated with arbitrary Weyl groups after localization. These generators yield non-graded KLR-like presentations of the modified algebras. As an application, we establish isomorphisms between direct sums of blocks of cyclotomic Hecke algebras of arbitrary Weyl groups and cyclotomic quotients of the resulting non-graded KLR-like algebras. We also explain how these isomorphisms identify the generalized weight-space decomposition of cyclotomic Hecke modules with the idempotent decomposition of modules over the KLR-like presentation.
