2013/11/30 by Kohei Motegi, Kazumitsu Sakai · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.MP #math.QA
paper · pdf · doi:10.1088/1751-8113/47/44/445202
published as J. Phys. A: Math. Theor. 47 (2014) 445202 · v4, 31 pages, 14 figures
arxiv created 2014/09/09 · arxiv updated 2014/10/17
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.