论文标题
主张Hecke代数及其表示
Affine Hecke algebras and their representations
论文作者
论文摘要
这是有关Aggine Hecke代数的调查文件。我们从头开始，讨论其代表理论的一些代数方面，指的是证明文献。我们尤其是针对不可约说明的分类。 只有最后，我们才建立一个新的结果：具有真实参数$ \ geq 1 $的仿射hecke代数的不可约表示的自然培养，以及代数为代数的仿射群体的不可约为表示。这可以被视为具有仿射Hecke代数的广义弹簧对应关系。
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible representations. Only at the end we establish a new result: a natural bijection between the set of irreducible representations of an affine Hecke algebra with real parameters $\geq 1$, and the set of irreducible representations of the affine Weyl group underlying the algebra. This can be regarded as a generalized Springer correspondence with affine Hecke algebras.
