p进群伯恩斯坦分支的赫克代数参数
表示论
2025-01-20 v4
摘要
设为非阿基米德局部域上的约化群。考虑复光滑-表示范畴中任意伯恩斯坦块Rep(G)^s。在早前工作中，作者证明了存在一个仿射赫克代数H(O,G)，其右模范畴与Rep(G)^s密切相关。在许多情形下这事实上是范畴等价，例如Iwahori-球表示。本文研究仿射赫克代数H(O,G)的q-参数。我们在许多情形下计算了它们，特别是拟分裂群的主级数表示以及经典群的情形。Lusztig猜想q-参数恒为q_F的整幂次，且与来自某无幂表示伯恩斯坦块的q-参数一致。我们将该猜想归约到单p进群的情形，并对其大多数情形予以证明。
引用
@article{arxiv.2103.13113,
title = {Parameters of Hecke algebras for Bernstein components of p-adic groups},
author = {Maarten Solleveld},
journal= {arXiv preprint arXiv:2103.13113},
year = {2025}
}
备注
Various minor improvements in Section 2. The proof of the previous Theorem 3.3 was flawed (in part c). Now that theorem is stretched over Lemma 3.3--Theorem 3.5. Proposition 4.10 was incorrect and has been repaired. At the same time, Theorem 4.9 has been simplified a little. In version 3, the paragraph 4.6 on F4 has been rewritten, now with more complete results