Non-Archimedean GUE corners and Hecke modules

Autor:	Shen, Jiahe, Van Peski, Roger
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Combinatorics Mathematics - Number Theory Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	We compute the joint distribution of singular numbers for all principal corners of a Hermitian (resp. alternating) matrix with additive Haar distribution over a non-archimedean local field, the non-archimedean analogue of the GUE (resp. aGUE) corners process. In the alternating case we find that it is a Hall-Littlewood process, explaining -- and recovering as a corollary -- results of Fulman-Kaplan. In the Hermitian case we obtain a `marginal distribution' of a formal Hall-Littlewood process with both positive and negative transition `probabilities'. The proofs relate natural random matrix operations to structural results of Hironaka and Hironaka-Sato on modules over the spherical Hecke algebra, yielding other probabilistic statements of independent interest along the way. Comment: 42 pages. Comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.05999 Zobrazit plný text záznamu View this record from Arxiv