


























We establish that the singular numbers (arising from Cartan decomposition) and corners (emerging from Iwasawa decomposition) in split reductive groups over non-archimedean fields are fundamentally determined by Hall-Littlewood polynomials. Through applications of the Satake isomorphism, we extend Van Peski's results (arXiv:2011.09356, Theorem 1.3) to encompass arbitrary root systems. Leveraging this theoretical foundation, we further develop Shen's work (arXiv:2411.01104, Theorem 1.1) to demonstrate that both singular numbers and corners of such products exhibit minimal separation. This characterization enables the derivation of asymptotic properties for singular numbers in matrix products, particularly establishing the strong law of large numbers and central limit theorem for these quantities. Our results provide a unified framework connecting algebraic decomposition structures with probabilistic limit theorems in non-archimedean settings.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。