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dc.contributor.author
Casper, W. Riley
dc.contributor.author
Grünbaum, Francisco Alberto
dc.contributor.author
Yakimov, Milen
dc.contributor.author
Zurrián, Ignacio Nahuel
dc.date.available
2022-10-12T15:34:17Z
dc.date.issued
2021-12
dc.identifier.citation
Casper, W. Riley; Grünbaum, Francisco Alberto; Yakimov, Milen; Zurrián, Ignacio Nahuel; Algebras of commuting differential operators for integral kernels of Airy type; Cornell University; arXiv; 12-2021; 1-19
dc.identifier.issn
2331-8422
dc.identifier.uri
http://hdl.handle.net/11336/172708
dc.description.abstract
Differential operators commuting with integral operators were discovered in the work of C. Tracy and H. Widom [37, 38] and used to derive asymptotic expansions of the Fredholm determinants of integral operators arising in random matrix theory. Very recently, it has been proved that all rational, symmetric Darboux transformations of the Bessel, Airy, and exponential bispectral functions give rise to commuting integral and differential operators [6, 7, 8], vastly generalizing the known examples in the literature. In this paper, we give a classification of the the rational symmetric Darboux transformations of the Airy function in terms of the fixed point submanifold of a differential Galois group acting on the Lagrangian locus of the (infinite dimensional) Airy Adelic Grassmannian and initiate the study of the full algebra of differential operators commuting with each of the integral operators in question. We leverage the general theory of [8] to obtain explicit formulas for the two differential operators of lowest orders that commute with each of the level one and two integral operators obtained in the Darboux process. Moreover, we prove that each pair of differential operators commute with each other. The commuting operators in the level one case are shown to satisfy an algebraic relation defining an elliptic curve.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Cornell University
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/
dc.subject
Mathematical physics
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Rings and algebras
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Spectral theory
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Algebras of commuting differential operators for integral kernels of Airy type
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-09-19T16:06:32Z
dc.journal.pagination
1-19
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Ithaca
dc.description.fil
Fil: Casper, W. Riley. California State University, Fullerton; Estados Unidos
dc.description.fil
Fil: Grünbaum, Francisco Alberto. University of California at Berkeley; Estados Unidos
dc.description.fil
Fil: Yakimov, Milen. Northeastern University; Estados Unidos
dc.description.fil
Fil: Zurrián, Ignacio Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.journal.title
arXiv
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.48550/arXiv.2112.11639
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2112.11639
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