Populations of Solutions to Cyclotomic Bethe Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Populations of Solutions to Cyclotomic Bethe Equations
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| Creator |
Varchenko, A.
Young, C.A.S. |
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| Description |
We study solutions of the Bethe Ansatz equations for the cyclotomic Gaudin model of [Vicedo B., Young C.A.S., 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 [Mukhin E., Varchenko A., Commun. Contemp. Math. 6 (2004), 111-163, math.QA/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 Z₂-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.
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| Date |
2019-02-13T16:57:57Z
2019-02-13T16:57:57Z 2015 |
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| Type |
Article
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| Identifier |
Populations of Solutions to Cyclotomic Bethe Equations / A. Varchenko, C.A.S Young // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 28 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 82B23; 32S22; 17B81; 81R12 DOI:10.3842/SIGMA.2015.091 http://dspace.nbuv.gov.ua/handle/123456789/147118 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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