Related papers: Virasoro constraints and polynomial recursion for …

In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important…

We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro constraints, which…

Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that the Q-polynomial expansion in this…

We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function. As an application, we obtain explicit formulas for all polynomial…

For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the…

We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed…

In this paper, we consider the higher Br\'ezin--Gross--Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac--Schwarz operators, quantum spectral curves, and $W^{(3)}$-constraints. For…

There is a general method for constructing a soliton hierarchy from a splitting of a loop group as a positive and a negative sub-groups together with a commuting linearly independent sequence in the positive Lie subalgebra. Many known…

For an arbitrary $p$, propose a new and computable method which can determine the values of unknown constants in constraints on a tau function which satisfies both the p-reduced KP hierarchy and the sting equation. All the constants do not…

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $\hat w$-operators. In this letter, we demonstrate that…

A $q$-analogue of the tau function of the modified KP hierarchy is defined by a change of independent variables. This tau function satisfies a system of bilinear $q$-difference equations. These bilinear equations are translated to the…

As the first step of proving the Hodge-FVH correspondence recently proposed in [19], we derive the Virasoro constraints and the Dubrovin--Zhang loop equation for special cubic Hodge integrals. We show that this loop equation has a unique…

We consider the Laguerre partition function, and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven that correlators have a…

We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B) which can be regarded as a discretization of the BKP hierarchy. We introduce the tau-function of the B-Toda hierarchy and obtain the bilinear…

Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on the claim that the situation is improved when integrability is enhanced to super-integrability,…

The purpose of this paper is to study Virasoro constraints for Hodge integrals in Gromov-Witten theory of any target varieties. Results consist of the following: Firstly, we propose Virasoro conjecture for Hodge integrals in Gromov-Witten…

Let $r\geq 2$ be an integer. The generalized BGW tau-function for the Gelfand--Dickey hierarchy of $(r-1)$ dependent variables (aka the $r$-reduced KP hierarchy) is defined as a particular tau-function that depends on $(r-1)$ constant…

We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…

We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\geq -1$ of the Lie algebra act by linear differential…

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field…