Related papers: The tau function for ABS equations

We present a formula for the connected \(n\)-point functions of a tau-funtion of the BKP hierarchy by embedding BKP hierarchy into KP hierarchy. This formula is different from the one given by Wang and Yang. We prove that these two formulae…

In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…

Sufficiently inclusive observables in the decay of the tau lepton can be calculated using the methods of perturbative QCD. These include the asymmetry parameter $A_\tau$ that determines that angular distribution of the total hadron momentum…

We show that the scalar product of the phase model is a (restricted) 2-Toda tau-function. Additionally, we highlight a correspondence between the boundary correlation functions of the model and the wave-functions of the hierarchy.

In this paper, we construct the quantum Torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum Torus Lie algebra in…

Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, "shift symmetries" of a quantum torus algebra plays a central…

We prove that P != NP by proving the existence of a class of functions we call Tau, each of whose members satisfies the conditions of one-way functions. Each member of Tau is a function computable in polynomial time, with negligible…

We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…

We construct a new class of operators that act on symmetric functions with two deformation parameters $q$ and $t$. Our combinatorial construction associates each operator with a specific lattice path, whose steps alternate between moving up…

We study derivatives of Schur and tau functions from the view point of the Abel-Jacobi map. We apply the results to establish several properties of derivatives of the sigma function of an (n,s) curve. As byproducts we have an expression of…

This note proposes an improved estimate of the coefficient t(n) of the discriminant modular form using elementary method. It improves a well known estimate of the tau function t(n) by Deligne.

In this short review the role of the Hirota equation and the tau-function in the theory of classical and quantum integrable systems is outlined.

The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied by the total descendant potential of $\mathbb{CP}^1$ with two orbifold points. We construct additional symmetries of the EBTH and describe explicitly their action…

The method of topological vertex for topological string theory on toric Calabi-Yau 3-folds is reviewed. Implications of an explicit formula of partition functions in the "on-strip" case, typically the generalized conifolds, are considered.…

For a simple Lie algebra $\mathfrak{g}$ and an irreducible faithful representation $\pi$ of $\mathfrak{g}$, we introduce the Schur polynomials of $(\mathfrak{g},\pi)$-type. We then derive the Sato-Zhou type formula for tau functions of the…

Weighted constellations give graphical representations of weighted branched coverings of the Riemann sphere. They were introduced to provide a combinatorial interpretation of the $2$D Toda $\tau$-functions of hypergeometric type serving as…

To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a Tau function. We then study their semiclassical expansion…

The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted…

The BV formalism is a well-established method for analyzing symmetries and quantization of field theories. In this paper we use the BV formalism to derive partition functions of gauge invariant operators up to equations of motions and their…

In this paper, we prove a conjecture of Alexandrov that the generalized Brezin-Gross-Witten tau-functions are hypergeometric tau functions of BKP hierarchy after re-scaling. In particular, this shows that the original BGW tau-function,…