Research on the representations of cyclotomic Hecke algebras and finite algebraic groups of classical type

我们确定了Hecke代数何时具有有限表示型。在经典类型中，Hecke代数具有类型B的情况是必不可少的，这种情况下的结果是基于我在2000年出版的书中解释的理论，在项目期间（特殊类型由Hyoue Miyachi解决）更准确地说，利用Dipper和Mathas的Morita等价定理，将证明归结为B型双参数Hecke代数有1和q^f作为参数。然后通过计算一些典型基元得到了一定的分解数。我们将联合收割机与Specht模理论和Artin代数理论相结合。因此我们有一个充分必要条件n<min（e，2f+4，2 e-2f+4），其中q是单位的本原eth根。经典型Hecke代数的结果作为这个结果的一个推论而得到.与此项目相关，我还发表了关于λ：Kleshchev <->D^λ*0的结果和关于combinatorios和晶体的论文，并完成了上述著作的英文翻译。这将由美国数学学会出版。

We have determined when a Hecke algebra has finite representation type. In classical types, the case where the Hecke algebra has type B is essential, and the result in this case is based on the theory which I explained in my book published in 2000, in the project term (Exceptional types were settled by Hyoue Miyachi)More precisely, using Morita equivalence theorem of Dipper and Mathas the proof is reduced to the case where a two-parameter Hecke algebra of type B has 1 and q^f as the parameters. Then we obtain certain decomposition numbers by the computation of some canonical basis elements. We combine this with Specht module theory and the theory of Artinian algebras. As a result we have a necessary and sufficient condition n<min (e, 2f+4, 2e-2f+4) where q is a primitive eth root of unity. Results for Hecke algebros of classical type are obtained as a Corollary of this result. Related to this project, I also published papers one on the result that λ : Kleshchev<->D^λ*0 the other on combinatorios and crystal.Moreover, I've completed the English translation of the book mentioned above. This will be published by the American Mathematical Society.