Completely Integrable Systems Associated with Classical Root Systems
We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the non-invariant systems, which include systems whose complete int...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147369 |
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| Cite this: | Completely Integrable Systems Associated with Classical Root Systems / T. Oshima // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Oshima, T. 2019-02-14T14:46:51Z 2019-02-14T14:46:51Z 2007 Completely Integrable Systems Associated with Classical Root Systems / T. Oshima // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R12; 70H06 https://nasplib.isofts.kiev.ua/handle/123456789/147369 We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the non-invariant systems, which include systems whose complete integrability will be first established in this paper. We also present a conjecture claiming that the quantum systems with enough integrals given in this note coincide with the systems that have the integrals with constant principal symbols corresponding to the homogeneous generators of the Bn-invariants. We review conditions supporting the conjecture and give a new condition assuring it. This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Completely Integrable Systems Associated with Classical Root Systems Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Completely Integrable Systems Associated with Classical Root Systems |
| spellingShingle |
Completely Integrable Systems Associated with Classical Root Systems Oshima, T. |
| title_short |
Completely Integrable Systems Associated with Classical Root Systems |
| title_full |
Completely Integrable Systems Associated with Classical Root Systems |
| title_fullStr |
Completely Integrable Systems Associated with Classical Root Systems |
| title_full_unstemmed |
Completely Integrable Systems Associated with Classical Root Systems |
| title_sort |
completely integrable systems associated with classical root systems |
| author |
Oshima, T. |
| author_facet |
Oshima, T. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the non-invariant systems, which include systems whose complete integrability will be first established in this paper. We also present a conjecture claiming that the quantum systems with enough integrals given in this note coincide with the systems that have the integrals with constant principal symbols corresponding to the homogeneous generators of the Bn-invariants. We review conditions supporting the conjecture and give a new condition assuring it.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147369 |
| citation_txt |
Completely Integrable Systems Associated with Classical Root Systems / T. Oshima // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 41 назв. — англ. |
| work_keys_str_mv |
AT oshimat completelyintegrablesystemsassociatedwithclassicalrootsystems |
| first_indexed |
2025-12-07T20:04:40Z |
| last_indexed |
2025-12-07T20:04:40Z |
| _version_ |
1850881218512420864 |