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arXiv · 1612.05361

Loop Models and $K$-Theory

Paul Zinn-Justin
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Abstract

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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Paul Zinn-Justin. 2016-12-16. Loop Models and $K$-Theory. https://doi.org/10.3842/sigma.2018.069

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