dc.contributor.author | Varchenko, Alexander | |
dc.contributor.author | Young, Charles A. S. | |
dc.date.accessioned | 2016-03-21T09:34:28Z | |
dc.date.available | 2016-03-21T09:34:28Z | |
dc.date.issued | 2015-11-14 | |
dc.identifier.citation | Varchenko , A & Young , C A S 2015 , ' Populations of solutions to cyclotomic Bethe equations ' , SIGMA , vol. 11 , 091 . https://doi.org/10.3842/SIGMA.2015.091 | |
dc.identifier.issn | 1815-0659 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1505.07582v1 | |
dc.identifier.other | ORCID: /0000-0002-7490-1122/work/55503485 | |
dc.identifier.uri | http://hdl.handle.net/2299/16822 | |
dc.description.abstract | We study solutions of the Bethe Ansatz equations for the cyclotomic Gaudin model of arXiv:1409.6937. We give two interpretations of such solutions: as critical points of a cyclotomic master function, and as critical points with cyclotomic symmetry of a certain "extended" master function. In finite types, this yields a correspondence between the Bethe eigenvectors and eigenvalues of the cyclotomic Gaudin model and those of an "extended" non-cyclotomic Gaudin model. We proceed to define populations of solutions to the cyclotomic Bethe equations, in the sense of arXiv:math/0209017, for diagram automorphisms of Kac-Moody Lie algebras. In the case of type A with the diagram automorphism, we associate to each population a vector space of quasi-polynomials with specified ramification conditions. This vector space is equipped with a Z_2-gradation and a non-degenerate bilinear form which is (skew-)symmetric on the even (resp. odd) graded subspace. We show that the population of cyclotomic critical points is isomorphic to the variety of isotropic full flags in this space. | en |
dc.format.extent | 41 | |
dc.format.extent | 388789 | |
dc.language.iso | eng | |
dc.relation.ispartof | SIGMA | |
dc.subject | math.QA | |
dc.title | Populations of solutions to cyclotomic Bethe equations | en |
dc.contributor.institution | School of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.identifier.url | http://arxiv.org/abs/1505.07582 | |
rioxxterms.versionofrecord | 10.3842/SIGMA.2015.091 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |