Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
复制标题
DOI：
10.1007/s00222-009-0204-8
复制
发表时间：
2008-08
影响因子：
3.1
通讯作者：
Jonathan Brundan;A. Kleshchev
中科院分区：
文献类型：
--
作者：
Jonathan Brundan;A. Kleshchev
本文构造了A型分圆Hecke代数和（符号修正）分圆Khovanov-Lauda代数的块之间的显式同构。这些同构将Khovanov和Lauda的范畴化猜想与Ariki的范畴化定理联系起来。Khovanov-Lauda代数是自然分次的，这使得我们可以在分圆Hecke代数的块上展示一个非平凡的分圆-分次，包括正特征的对称群。
We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial ℤ-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.