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
Date:2007
Main Author: Oshima, T.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147369
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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 nasplib_isofts_kiev_ua-123456789-147369
record_format dspace
spelling 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
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