非阿基米德 GUE 角块与 Hecke 模
概率论
2025-04-17 v2 组合数学
数论
表示论
摘要
我们计算了具有加法 Haar 分布的 p-adic Hermitian（resp. alternating）矩阵的所有主角块的奇异数的联合分布，这是 GUE（resp. aGUE）角块过程的非阿基米德类比。在交替情形下，我们发现它是一个 Hall-Littlewood 过程，解释并作为推论恢复了 Fulman-Kaplan 的结果。在 Hermitian 情形下，我们获得了形式 Hall-Littlewood 过程的边缘分布，其具有正负两种转移概率。证明将自然的随机矩阵运算与球面 Hecke 代数上模的结构结果联系起来，沿途产生了其他具有独立概率意义的命题。
引用
@article{arxiv.2412.05999,
title = {Non-Archimedean GUE corners and Hecke modules},
author = {Jiahe Shen and Roger Van Peski},
journal= {arXiv preprint arXiv:2412.05999},
year = {2025}
}
备注
43 pages. v2: correction to v1, which erroneously stated that the proofs were valid in positive characteristic as well as for p-adic fields. The new Appendix A explains what details are missing from the literature which would be needed to conclude this. Various other minor typos corrected