(glM,glN)-Dualities in Gaudin Models with Irregular Singularities
We establish (glM,glN)-dualities between quantum Gaudin models with irregular singularities. Specifically, for any M,N ∈ Z≥1, we consider two Gaudin models: the one associated with the Lie algebra glM, which has a double pole at infinity and N poles, counting multiplicities, in the complex plane, an...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209532 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | (glM,glN)-Dualities in Gaudin Models with Irregular Singularities / B. Vicedo, C. Young // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-209532 |
|---|---|
| record_format |
dspace |
| spelling |
Vicedo, B. Young, C. 2025-11-24T10:43:43Z 2018 (glM,glN)-Dualities in Gaudin Models with Irregular Singularities / B. Vicedo, C. Young // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B80; 81R12; 82B23 arXiv: 1710.08672 https://nasplib.isofts.kiev.ua/handle/123456789/209532 https://doi.org/10.3842/SIGMA.2018.040 We establish (glM,glN)-dualities between quantum Gaudin models with irregular singularities. Specifically, for any M,N ∈ Z≥1, we consider two Gaudin models: the one associated with the Lie algebra glM, which has a double pole at infinity and N poles, counting multiplicities, in the complex plane, and the same model but with the roles of M and N interchanged. Both models can be realized in terms of Weyl algebras, i.e., free bosons; we establish that, in this realization, the algebras of integrals of motion of the two models coincide. At the classical level, we establish two further generalizations of the duality. First, we show that there is also a duality for realizations in terms of free fermions. Second, in the bosonic realization, we consider the classical cyclotomic Gaudin model associated with the Lie algebra glM and its diagram automorphism, with a double pole at infinity and 2N poles, counting multiplicities, in the complex plane. We prove that it is dual to a non-cyclotomic Gaudin model associated with the Lie algebra sp2N, with a double pole at infinity and M simple poles in the complex plane. In the special case N=1, we recover the well-known self-duality in the Neumann model. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications (glM,glN)-Dualities in Gaudin Models with Irregular Singularities Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities |
| spellingShingle |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities Vicedo, B. Young, C. |
| title_short |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities |
| title_full |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities |
| title_fullStr |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities |
| title_full_unstemmed |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities |
| title_sort |
(glm,gln)-dualities in gaudin models with irregular singularities |
| author |
Vicedo, B. Young, C. |
| author_facet |
Vicedo, B. Young, C. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We establish (glM,glN)-dualities between quantum Gaudin models with irregular singularities. Specifically, for any M,N ∈ Z≥1, we consider two Gaudin models: the one associated with the Lie algebra glM, which has a double pole at infinity and N poles, counting multiplicities, in the complex plane, and the same model but with the roles of M and N interchanged. Both models can be realized in terms of Weyl algebras, i.e., free bosons; we establish that, in this realization, the algebras of integrals of motion of the two models coincide. At the classical level, we establish two further generalizations of the duality. First, we show that there is also a duality for realizations in terms of free fermions. Second, in the bosonic realization, we consider the classical cyclotomic Gaudin model associated with the Lie algebra glM and its diagram automorphism, with a double pole at infinity and 2N poles, counting multiplicities, in the complex plane. We prove that it is dual to a non-cyclotomic Gaudin model associated with the Lie algebra sp2N, with a double pole at infinity and M simple poles in the complex plane. In the special case N=1, we recover the well-known self-duality in the Neumann model.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209532 |
| citation_txt |
(glM,glN)-Dualities in Gaudin Models with Irregular Singularities / B. Vicedo, C. Young // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. |
| work_keys_str_mv |
AT vicedob glmglndualitiesingaudinmodelswithirregularsingularities AT youngc glmglndualitiesingaudinmodelswithirregularsingularities |
| first_indexed |
2025-12-07T17:01:03Z |
| last_indexed |
2025-12-07T17:01:03Z |
| _version_ |
1850886082178056192 |