Indagationes Mathematicae ( IF 0.5 ) Pub Date : 2021-01-22 , DOI: 10.1016/j.indag.2021.01.005 Maarten Solleveld
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 parameters in , 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.
中文翻译:
仿射赫克代数及其表示
这是一篇关于仿射 Hecke 代数的调查论文。我们从头开始讨论他们的表示理论的一些代数方面,参考文献进行证明。我们特别针对不可约表示的分类。
直到最后我们才建立一个新的结果:一个仿射 Hecke 代数的不可约表示集之间的自然双射 ,以及代数基础的仿射 Weyl 群的不可约表示集。这可以看作是与仿射 Hecke 代数的广义 Springer 对应关系。