Vertex Operators and Solvable Lattice Models
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Vertex operators originally arose in mathematical physics (string theory and soliton theory). They were applied to construct representations of affine Lie algebras by I. Frenkel and Kac, and an important algebraic fact emerged, the "boson-fermion correspondence". This concerns a Hamiltonian operator on the "fermionic Fock space". In some cases such a Hamiltonian can be related to the row transfer matrix for a solvable lattice model. The archetype for such a relation is Baxter's work relating the XYZ Hamiltonian with the 8-vertex model. A recent (2017) example is arXiv:1806.07776 where Brubaker, Buciumas, Bump and Gustafsson proved that the row transfer matrices of certain models motivated by the theory of metaplectic Whittaker functions could be realized by vertex operators on a version of the fermionic Fock space invented by Kashiwara, Miwa and Stern, that was previously applied by Lascoux, Leclerc and Thibon in the theory of ribbon symmetric functions.
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