Loop Models and $K$-Theory

Symmetry Integrability and Geometry-Methods and Applications

article

Paul Zinn-Justin¹ 

[1] School of Mathematics and Statistics, The University of Melbourne

关键词: quantum integrability;    loop models;    K-theory;   

DOI  :  10.3842/SIGMA.2018.069

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown