63 research outputs found
K-theoretic boson-fermion correspondence and melting crystals
We study non-Hermitian integrable fermion and boson systems from the
perspectives of Grothendieck polynomials. The models considered in this article
are the five-vertex model as a fermion system and the non-Hermitian phase model
as a boson system. Both of the models are characterized by the different
solutions satisfying the same Yang-Baxter relation. From our previous works on
the identification between the wavefunctions of the five-vertex model and
Grothendieck polynomials, we introduce skew Grothendieck polynomials, and
derive the addition theorem among them. Using these relations, we derive the
wavefunctions of the non-Hermitian phase model as a determinant form which can
also be expressed as the Grothendieck polynomials. Namely, we establish a
K-theoretic boson-fermion correspondence at the level of wavefunctions. As a
by-product, the partition function of the statistical mechanical model of a 3D
melting crystal is exactly calculated by use of the scalar products of the
wavefunctions of the phase model. The resultant expression can be regarded as a
K-theoretic generalization of the MacMahon function describing the generating
function of the plane partitions, which interpolates the generating functions
of two-dimensional and three-dimensional Young diagrams.Comment: v4, 31 pages, 14 figure
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