τ-Functions, Birkhoff Factorizations and Difference Equations
Q-systems and T-systems are systems of integrable difference equations that have recently attracted much attention and have wide applications in representation theory and statistical mechanics. We show that certain τ-functions, given as matrix elements of the action of the loop group of GL₂ on two-c...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210052 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | τ-Functions, Birkhoff Factorizations and Difference Equations / D. Addabbo, M. Bergvelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862555453024632832 |
|---|---|
| author | Addabbo, D. Bergvelt, M. |
| author_facet | Addabbo, D. Bergvelt, M. |
| citation_txt | τ-Functions, Birkhoff Factorizations and Difference Equations / D. Addabbo, M. Bergvelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Q-systems and T-systems are systems of integrable difference equations that have recently attracted much attention and have wide applications in representation theory and statistical mechanics. We show that certain τ-functions, given as matrix elements of the action of the loop group of GL₂ on two-component fermionic Fock space, give solutions of a Q-system. An obvious generalization using the loop group of GL₃ acting on three-component fermionic Fock space leads to a new system of 4 difference equations.
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| first_indexed | 2025-12-07T21:24:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210052 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:12Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Addabbo, D. Bergvelt, M. 2025-12-02T09:28:44Z 2019 τ-Functions, Birkhoff Factorizations and Difference Equations / D. Addabbo, M. Bergvelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B80 arXiv: 1605.00192 https://nasplib.isofts.kiev.ua/handle/123456789/210052 https://doi.org/10.3842/SIGMA.2019.023 Q-systems and T-systems are systems of integrable difference equations that have recently attracted much attention and have wide applications in representation theory and statistical mechanics. We show that certain τ-functions, given as matrix elements of the action of the loop group of GL₂ on two-component fermionic Fock space, give solutions of a Q-system. An obvious generalization using the loop group of GL₃ acting on three-component fermionic Fock space leads to a new system of 4 difference equations. The authors gratefully acknowledge travel support from the Simons Foundation, Collaboration Grant 245048. Addabbo expresses thanks for support from Dr. Lois M. Lackner Mathematics Fellowships, the University of Illinois Research Board, and the Associate Alumnae of Douglass College. The authors also thank Philippe Di Francesco and Rinat Kedem for helpful conversations, and anonymous referees for many helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications τ-Functions, Birkhoff Factorizations and Difference Equations Article published earlier |
| spellingShingle | τ-Functions, Birkhoff Factorizations and Difference Equations Addabbo, D. Bergvelt, M. |
| title | τ-Functions, Birkhoff Factorizations and Difference Equations |
| title_full | τ-Functions, Birkhoff Factorizations and Difference Equations |
| title_fullStr | τ-Functions, Birkhoff Factorizations and Difference Equations |
| title_full_unstemmed | τ-Functions, Birkhoff Factorizations and Difference Equations |
| title_short | τ-Functions, Birkhoff Factorizations and Difference Equations |
| title_sort | τ-functions, birkhoff factorizations and difference equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210052 |
| work_keys_str_mv | AT addabbod τfunctionsbirkhofffactorizationsanddifferenceequations AT bergveltm τfunctionsbirkhofffactorizationsanddifferenceequations |