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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Zinn-Justin, P.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209781
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Loop Models and K-Theory / P. Zinn-Justin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 40 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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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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