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 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2013
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| 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| id |
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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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