Non-Archimedean GUE corners and Hecke modules
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908321498267648 |
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| author | Shen, Jiahe Van Peski, Roger |
| author_facet | Shen, Jiahe Van Peski, Roger |
| contents | We compute the joint distribution of singular numbers for all principal corners of a $p$-adic Hermitian (resp. alternating) matrix with additive Haar distribution, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Archimedean GUE corners and Hecke modules Shen, Jiahe Van Peski, Roger Probability Combinatorics Number Theory Representation Theory We compute the joint distribution of singular numbers for all principal corners of a $p$-adic Hermitian (resp. alternating) matrix with additive Haar distribution, 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. |
| title | Non-Archimedean GUE corners and Hecke modules |
| topic | Probability Combinatorics Number Theory Representation Theory |
| url | https://arxiv.org/abs/2412.05999 |