For a connected reductive group G defined over a non-archimedean local field F , we consider the Bernstein blocks in the category of smooth representations of G⁢(F){G(F)}. Bernstein blocks whose cuspidal support involves a regular supercuspidal representation are called regular Bernstein blocks. Most Bernstein blocks are regular when the residual characteristic of F is not too small. Under mild hypotheses on the residual characteristic, we show that the Bernstein center of a regular Bernstein block of G⁢(F){G(F)} is isomorphic to the Bernstein center of a regular depth-zero Bernstein block of G0⁢(F){G^{0}(F)}, where G0{G^{0}} is a certain twisted Levi subgroup of G . In some cases, we show that the blocks themselves are equivalent, and as a consequence we prove the ABPS Conjecture in some new cases.

中文翻译：

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常规伯恩斯坦块

对于定义在非阿基米德局部域 F 上的连通归约群 G，我们考虑 G⁢(F){G(F)} 的平滑表示类别中的 Bernstein 块。其尖点支持涉及常规超尖点表示的 Bernstein 块称为常规 Bernstein 块。当 F 的残差特征不太小时，大多数 Bernstein 块是规则的。在对残差特征的温和假设下，我们证明 G⁢(F){G(F)} 的规则 Bernstein 块的 Bernstein 中心与 G0⁢(F){G(F)} 的规则深度为零的 Bernstein 块的 Bernstein 中心同构）{G ^ {0}（F）}，其中G0 {G ^ {0}}是G的某个扭曲的Levi子群。在某些情况下，我们证明了这些块本身是等效的，因此，我们在某些新情况下证明了ABPS猜想。