On the representation theory of Iwahori-Hecke algebras of extended finite Weyl groups
On the representation theory of Iwahori-Hecke algebras of extended finite Weyl groups
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DOI：
10.1090/s1088-4165-00-00093-5
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发表时间：
2000-09
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影响因子：
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通讯作者：
M. Geck
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文献类型：
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作者：
M. Geck
我们将 Lusztig 的细胞理论和渐近代数应用于由一组图自同构扩展的有限 Weyl 群的 Iwahori-Hecke 代数。这产生了关于分裂场（扩展迪涅-米歇尔早期结果）和分解矩阵（概括作者早期结果）的一般结果。我们的主要应用是利用 Dipper、James、Murphy、Ariki 和 Mathas 得出的有关 Bn 类型的已知结果，为 Dn 类型中的简单模块的数量（特征 2 除外）建立一个显式公式。
We apply Lusztig’s theory of cells and asymptotic algebras to the Iwahori–Hecke algebra of a finite Weyl group extended by a group of graph automorphisms. This yields general results about splitting fields (extending earlier results by Digne–Michel) and decomposition matrices (generalizing earlier results by the author). Our main application is to establish an explicit formula for the number of simple modules in type Dn (except in characteristic 2), using the known results about type Bn due to Dipper, James, and Murphy and Ariki and Mathas.