Loop Models and K-Theory
This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant K-theory of the cotangent bundle of the Grassmannian. We interpret various concepts from integrable systems (R-...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2018 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209781 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Loop Models and K-Theory / P. Zinn-Justin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 40 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727340529811456 |
|---|---|
| author | Zinn-Justin, P. |
| author_facet | Zinn-Justin, P. |
| citation_txt | Loop Models and K-Theory / P. Zinn-Justin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 40 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant K-theory of the cotangent bundle of the Grassmannian. We interpret various concepts from integrable systems (R-matrix, partition function on a finite domain) in geometric terms. As a byproduct, we provide explicit formulae for K-classes of various coherent sheaves, including structure and (conjecturally) square roots of canonical sheaves and canonical sheaves of conormal varieties of Schubert varieties.
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| first_indexed | 2025-12-07T19:02:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209781 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:02:35Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zinn-Justin, P. 2025-11-26T12:19:33Z 2018 Loop Models and K-Theory / P. Zinn-Justin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14M15; 82B23 arXiv: 1612.05361 https://nasplib.isofts.kiev.ua/handle/123456789/209781 https://doi.org/10.3842/SIGMA.2018.069 This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant K-theory of the cotangent bundle of the Grassmannian. We interpret various concepts from integrable systems (R-matrix, partition function on a finite domain) in geometric terms. As a byproduct, we provide explicit formulae for K-classes of various coherent sheaves, including structure and (conjecturally) square roots of canonical sheaves and canonical sheaves of conormal varieties of Schubert varieties. PZJ was supported by ERC grant 278124 and ARC grant FT150100232. Computerized checks of the results of this paper were performed with the help of Macaulay 2 [15]. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Loop Models and K-Theory Article published earlier |
| spellingShingle | Loop Models and K-Theory Zinn-Justin, P. |
| title | Loop Models and K-Theory |
| title_full | Loop Models and K-Theory |
| title_fullStr | Loop Models and K-Theory |
| title_full_unstemmed | Loop Models and K-Theory |
| title_short | Loop Models and K-Theory |
| title_sort | loop models and k-theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209781 |
| work_keys_str_mv | AT zinnjustinp loopmodelsandktheory |