Related papers: Multiple integral formula for the off-shell six ve…

Continuing our work hep-th/9609135 where a explicit formula for the two-point functions of the two dimensional Z-invariant Ising model were found. I obtain here different results for the higher correlation functions and several consistency…

We present families of single determinantal representations of on-shell scalar products of Bethe vectors. Our families of representations are parameterized by a continuous complex variable which can be fixed at convenience. Here we consider…

In this paper, we systematically investigate the multidimensional $Z$-transform of functions with values in sequentially complete locally convex spaces over the field of complex numbers. We provide many structural characterizations, remarks…

We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities…

We prove that the multiple summing norm of multilinear operators defined on some $n$-dimensional real or complex vector spaces with the $p$-norm may be written as an integral with respect to stables measures. As an application we show…

In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…

We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular integrals [7]. For the variable exponent case, a key element…

A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $\Delta$. We present a new algorithm for computing closed-form formulas for vector…

We classify the 3-point functions of local gauge-invariant single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills involving at least one su(3) operator. In the case of two su(3) and one su(2) operators, the…

We consider the open problem of determining the graded Betti numbers for fat point subschemes supported at general points of the projective plane. We relate this problem to the open geometric problem of determining the splitting type of the…

In this work we obtain hierarchies of partial differential equations describing on-shell scalar products for two types of six-vertex models. More precisely, six-vertex models with two different diagonal boundary conditions are considered:…

We obtain an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase region. The proof is based on a formula for the partition function involving the…

The deformation approach of arXiv:2104.07816 for computing zeta functions of one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter manifolds. Consideration of the multiparameter case requires the development of an…

We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…

Partition function of beta-gamma systems on the orbifolds C^2/Z_N and C^3/Z_M x Z_N are obtained as the invariant part of that on the respective affine spaces, by lifting the geometric action of the orbifold group to the fields.…

We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies…

In this paper, we provide formulas to calculate the partition functions of two types of plane partitions using the crystal melting model introduced by Okounkov, Reshetikhin and Vafa. As applications, we obtain a product formula for the…

We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$…

Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures.…

It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also…