Related papers: Elliptic supersymmetric integrable model and multi…
We introduce and investigate a class of $\mathfrak{gl}_{M+1}$ partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested version of Izergin-Korepin analysis, and…
We analyze the scalar products of the elliptic Felderhof model introduced by Foda-Wheeler-Zuparic as an elliptic extension of the trigonometric face-type Felderhof model by Deguchi-Akutsu. We derive the determinant formula for the scalar…
Recently, a class of partition functions associated with higher rank rational and trigonometric integrable models were introduced by Foda and Manabe. We use the dynamical $R$-matrix of the elliptic quantum group $E_{\tau,\eta}(gl_3)$ to…
We prove a duality formula between two elliptic determinants. We present a proof which is a variant of the Izergin-Korepin method which is a method originally introduced to analyze and compute partition functions of integrable lattice…
We examine the group theoretical reason why various two dimensional statistical integrable models, such as the Ising model, the chiral Potts model and the Belavin model, becomes integrable. The symmetry of these integrable models is SU(2)…
Fully inhomogeneous spin Hall-Littlewood symmetric rational functions $\mathsf{F}_\lambda$ arise in the context of $\mathfrak{sl}(2)$ higher spin six vertex models, and are multiparameter deformations of the classical Hall-Littlewood…
As a necessary step in constructing elliptic matrix models, which preserve the superintegrability property $<char>\sim {\rm char}$, we suggest an elliptic deformation of the peculiar loci $p_k^{\Delta_n}$, which play an important role in…
We discuss elliptic quantum Calogero-Moser-Sutherland models, including their relativistic generalizations due to Ruijsenaars and van Diejen, and the relations of these models to classes of special functions developed and explored in recent…
The conjectures of Deligne, Be\u\i linson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their $L$-functions. We make a numerical study for symmetric power…
Two dimensional statistical integrable models, such as the Ising model, the chiral Potts model and the Belavin model, becomes integrable. Because of the SU(2) symmetry of these models, these models become integrable. The integral models are…
We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…
We study a linear map on symmetric functions that ``divides'' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partitions of $n$. We determine its Schur…
As a development of arXiv:1912.12897, we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic system (Dell). The lacking parameter can be provided by…
We obtain factorized domain wall partition functions in two elliptic height models: 1. A Felderhof-type model, which is new, and 2. A Perk-Schultz-type gl(1|1) model of Deguchi and Martin.
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
We describe a Yang-Baxter integrable vertex model, which can be realized as a degeneration of a vertex model introduced by Aggarwal, Borodin, and Wheeler. From this vertex model, we construct a certain class of partition functions that we…
Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…
We construct a vertex model whose partition function is a refined dual Grothendieck polynomial, where the states are interpreted as nonintersecting lattice paths. Using this, we show refined dual Grothendieck polynomials are multi-Schur…
We review and present new studies on the relation between the partition functions of integrable lattice models and symmetric polynomials, and its combinatorial representation theory based on the correspondence, including our work. In…
We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are…