Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method
For each affine Kac-Moody algebra ⁽ʳ⁾ₙ of rank ℓ, = 1,2, or 3, and for every choice of a vertex ₘ, = 0, …, ℓ, of the corresponding Dynkin diagram, by using the matrix-resolvent method, we define a gauge-invariant tau-structure for the associated Drinfeld-Sokolov hierarchy and give explicit formula...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2022 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2022
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211827 |
| 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: | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method. Boris Dubrovin, Daniele Valeri and Di Yang. SIGMA 18 (2022), 077, 32 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741565590470656 |
|---|---|
| author | Dubrovin, Boris Valeri, Daniele Yang, Di |
| author_facet | Dubrovin, Boris Valeri, Daniele Yang, Di |
| citation_txt | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method. Boris Dubrovin, Daniele Valeri and Di Yang. SIGMA 18 (2022), 077, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For each affine Kac-Moody algebra ⁽ʳ⁾ₙ of rank ℓ, = 1,2, or 3, and for every choice of a vertex ₘ, = 0, …, ℓ, of the corresponding Dynkin diagram, by using the matrix-resolvent method, we define a gauge-invariant tau-structure for the associated Drinfeld-Sokolov hierarchy and give explicit formulas for generating series of logarithmic derivatives of the tau-function in terms of matrix resolvents, extending the results of [Mosc. Math. J. 21 (2021), 233-270, arXiv:1610.07534] with = 1 and = 0. For the case = 1 and = 0, we verify that the above-defined tau-structure agrees with the axioms of Hamiltonian tau-symmetry in the sense of [Adv. Math. 293 (2016), 382-435, arXiv:1409.4616] and [arXiv:math.DG/0108160].
|
| first_indexed | 2026-04-17T17:59:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211827 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T17:59:49Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dubrovin, Boris Valeri, Daniele Yang, Di 2026-01-12T10:22:17Z 2022 Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method. Boris Dubrovin, Daniele Valeri and Di Yang. SIGMA 18 (2022), 077, 32 pages 1815-0659 2020 Mathematics Subject Classification: 37K10; 17B80; 17B67; 37K30 arXiv:2110.06655 https://nasplib.isofts.kiev.ua/handle/123456789/211827 https://doi.org/10.3842/SIGMA.2022.077 For each affine Kac-Moody algebra ⁽ʳ⁾ₙ of rank ℓ, = 1,2, or 3, and for every choice of a vertex ₘ, = 0, …, ℓ, of the corresponding Dynkin diagram, by using the matrix-resolvent method, we define a gauge-invariant tau-structure for the associated Drinfeld-Sokolov hierarchy and give explicit formulas for generating series of logarithmic derivatives of the tau-function in terms of matrix resolvents, extending the results of [Mosc. Math. J. 21 (2021), 233-270, arXiv:1610.07534] with = 1 and = 0. For the case = 1 and = 0, we verify that the above-defined tau-structure agrees with the axioms of Hamiltonian tau-symmetry in the sense of [Adv. Math. 293 (2016), 382-435, arXiv:1409.4616] and [arXiv:math.DG/0108160]. Part of the work of D.V. and D.Y. was done during their visits to SISSA and Tsinghua University during the years 2017 and 2018; they thank both SISSA and Tsinghua for warm hospitality and financial support. D.V. acknowledges the financial support of the project MMNLP (Mathematical Methods in Non Linear Physics) of the INFN. The work of D.Y. was partially supported by the National Key R and D Program of China 2020YFA0713100, and by NSFC 12061131014. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method Article published earlier |
| spellingShingle | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method Dubrovin, Boris Valeri, Daniele Yang, Di |
| title | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method |
| title_full | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method |
| title_fullStr | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method |
| title_full_unstemmed | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method |
| title_short | Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method |
| title_sort | affine kac-moody algebras and tau-functions for the drinfeld-sokolov hierarchies: the matrix-resolvent method |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211827 |
| work_keys_str_mv | AT dubrovinboris affinekacmoodyalgebrasandtaufunctionsforthedrinfeldsokolovhierarchiesthematrixresolventmethod AT valeridaniele affinekacmoodyalgebrasandtaufunctionsforthedrinfeldsokolovhierarchiesthematrixresolventmethod AT yangdi affinekacmoodyalgebrasandtaufunctionsforthedrinfeldsokolovhierarchiesthematrixresolventmethod |