A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy

We show that the (semi-infinite) Ablowitz-Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508-1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero,...

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Дата:2013
Автори: Haine, L., Vanderstichelen, D.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2013
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/149371
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy / L. Haine, D. Vanderstichelen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1493712019-02-22T01:23:35Z A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy Haine, L. Vanderstichelen, D. We show that the (semi-infinite) Ablowitz-Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508-1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero, Moral and Velázquez (CMV) matrices [Linear Algebra Appl. 362 (2003), 29-56] and their action on the tau-functions of the hierarchy is described. The use of the CMV matrices turns out to be crucial for obtaining a Lax pair representation of the master symmetries. The AL hierarchy seems to be the first example of an integrable hierarchy which admits a full centerless Virasoro algebra of master symmetries, in contrast with the Toda lattice and Korteweg-de Vries hierarchies which possess only ''half of'' a Virasoro algebra of master symmetries, as explained in Adler and van Moerbeke [Duke Math. J. 80 (1995), 863-911], Damianou [Lett. Math. Phys. 20 (1990), 101-112] and Magri and Zubelli [Comm. Math. Phys. 141 (1991), 329-351]. 2013 Article A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy / L. Haine, D. Vanderstichelen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 17B68 DOI: http://dx.doi.org/10.3842/SIGMA.2013.079 http://dspace.nbuv.gov.ua/handle/123456789/149371 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We show that the (semi-infinite) Ablowitz-Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508-1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero, Moral and Velázquez (CMV) matrices [Linear Algebra Appl. 362 (2003), 29-56] and their action on the tau-functions of the hierarchy is described. The use of the CMV matrices turns out to be crucial for obtaining a Lax pair representation of the master symmetries. The AL hierarchy seems to be the first example of an integrable hierarchy which admits a full centerless Virasoro algebra of master symmetries, in contrast with the Toda lattice and Korteweg-de Vries hierarchies which possess only ''half of'' a Virasoro algebra of master symmetries, as explained in Adler and van Moerbeke [Duke Math. J. 80 (1995), 863-911], Damianou [Lett. Math. Phys. 20 (1990), 101-112] and Magri and Zubelli [Comm. Math. Phys. 141 (1991), 329-351].
format Article
author Haine, L.
Vanderstichelen, D.
spellingShingle Haine, L.
Vanderstichelen, D.
A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Haine, L.
Vanderstichelen, D.
author_sort Haine, L.
title A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
title_short A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
title_full A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
title_fullStr A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
title_full_unstemmed A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
title_sort centerless virasoro algebra of master symmetries for the ablowitz-ladik hierarchy
publisher Інститут математики НАН України
publishDate 2013
url http://dspace.nbuv.gov.ua/handle/123456789/149371
citation_txt A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy / L. Haine, D. Vanderstichelen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
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AT vanderstichelend centerlessvirasoroalgebraofmastersymmetriesfortheablowitzladikhierarchy
first_indexed 2023-05-20T17:32:50Z
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