Ciubotaru Dan
Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK.
Invent Math. 2018;213(1):237-269. doi: 10.1007/s00222-018-0790-4. Epub 2018 Feb 1.
We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. Moreover, we show that every irreducible smooth -representation contains a rigid type. This is a generalization of the unitarity criterion of Barbasch and Moy for representations with Iwahori fixed vectors.
我们证明，对于满足特定刚性假设的每个布什内尔 - 库茨科类型，相应伯恩斯坦分量与该类型赫克代数的模的范畴之间的范畴等价性，在这两个范畴的不可约酉表示之间诱导出一个双射。此外，我们表明每个不可约光滑 - 表示都包含一个刚性类型。这是巴尔巴什和莫伊关于具有岩泽固定向量的表示的酉性准则的推广。
