Loop Models and K-Theory
Copyright policy )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 ($R$-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.
- University of Melbourne Australia
Applications of methods of algebraic \(K\)-theory in algebraic geometry, Classical problems, Schubert calculus, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, FOS: Physical sciences, \(K\)-theory, Mathematical Physics (math-ph), Grassmannians, Schubert varieties, flag manifolds, Relationships between surfaces, higher-dimensional varieties, and physics, quantum integrability, loop models, Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Exactly solvable models; Bethe ansatz, Algebraic Geometry (math.AG), Miscellaneous applications of \(K\)-theory, Mathematical Physics
Applications of methods of algebraic \(K\)-theory in algebraic geometry, Classical problems, Schubert calculus, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, FOS: Physical sciences, \(K\)-theory, Mathematical Physics (math-ph), Grassmannians, Schubert varieties, flag manifolds, Relationships between surfaces, higher-dimensional varieties, and physics, quantum integrability, loop models, Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Exactly solvable models; Bethe ansatz, Algebraic Geometry (math.AG), Miscellaneous applications of \(K\)-theory, Mathematical Physics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!