Satake型同构与Bernstein型同构在特征p上的相容性
Compatibility between Satake and Bernstein-type isomorphisms in characteristic p
摘要：
研究了连通分裂p-adic约化群G的pro-pIwahori-Hecke环H的中心.对特征为p的代数闭域k，证明了k-代数H_k：= H \otimes_Z k的中心包含一个仿射半群代数，该仿射半群代数自然同构于G的超特殊极大紧子群的任一不可约光滑k-表示上的Hecke代数.这个同构使用arXiv：1207.5557中构造的逆Satake同构获得。我们应用这一结果对简单超奇异H_k-模进行了分类，研究了有限长H_k-模范畴中的超奇异块，并将后者与G的超奇异表示联系起来。
英文摘要：
We study the center of the pro-p Iwahori-Hecke ring H of a connected split p-adic reductive group G. For k an algebraically closed field with characteristic p, we prove that the center of the k-algebra H_k:= H\otimes_Z k contains an affine semigroup algebra which is naturally isomorphic to the Hecke algebra attached to any irreducible smooth k-representation of a given hyperspecial maximal compact subgroup of G. This isomorphism is obtained using the inverse Satake isomorphism constructed in arXiv:1207.5557. We apply this to classify the simple supersingular H_k-modules, study the supersingular block in the category of finite length H_k-modules, and relate the latter to supersingular representations of G.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
