相关论文: Giambelli type formulae in the BKP hierarchy

We prove existence of the tau-function for the multi-component CKP hierarchy and find how it is related to the tau-function of the multi-component KP hierarchy.

In this paper, we extend the matrix-resolvent method to the study of the Dubrovin--Zhang type tau-functions for the constrained KP hierarchy and the bigraded Toda hierarchy of $(M,1)$-type. We show that the Dubrovin--Zhang type tau-function…

It is proved that the action for nonlinear Beltrami equation (quasiclassical dbar-problem) evaluated on its solution gives a tau-function for dispersionless KP hierarchy. Infinitesimal transformations of tau-function corresponding to…

Using the bilinear formalism, we consider multicomponent and matrix modified KP hierarchies. The main tool is the bilinear identity for the tau-function which is realized as an expectation value of a Clifford group element composed from…

The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling…

We propose a new representation of the fourth Painlev\'e equation in which the $A^{(1)}_2$-symmetries become clearly visible. By means of this representation, we clarify the internal relation between the fourth Painlev\'e equation and the…

It was proved in 2010 that the principal Kac--Wakimoto hierarchy of type $D$ is a reduction of the 2-component BKP hierarchy. On the other hand, it is known that the total descendant potential of a singularity of type $D$ is a tau-function…

An element [\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\phi} for C(x). The Pl\"ucker coordinates…

In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau functions of higher…

Jacobi-Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised Schur polynomials.

In 2015, Jing and Li defined type B quasisymmetric Schur functions and conjectured that these functions have a positive, integral and unitriangular expansion into peak functions. We prove this conjecture, and refine their combinatorial…

We give a straightforward derivation of the string equation and Virasoro constraints on the $\tau$ function of the BKP hierarchy by means of some special additional symmetry flows. The explicit forms of the actions of these additional…

We prove that the supersymmetric BKP-hierarchy of Yu (SBKP_2) is hamiltonian with respect to a nonlinear extension of the N=1 Super-Virasoro algebra (W_SBKP) by fields of spin k, where k>3/2 and 2k = 0,3 mod 4. Moreover, we show how to…

The KP hierarchy is a completely integrable system of quadratic, partial differential equations that generalizes the KdV hierarchy. A linear combination of Schur functions is a solution to the KP hierarchy if and only if its coefficients…

We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies…

A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear…

We study the tau function of the KP-hierarchy associated with an (n,1) curve $y^n=x-\alpha$. If $\alpha=0$ the corresponding tau function is 1. On the other hand if $\alpha\neq 0$ the tau function becomes the exponential of a quadratic…

We construct all polynomial tau-functions of the BKP, DKP and MDKP hierarches.

In this paper, we prove that the generalized Br\'ezin-Gross-Witten tau-function is a hypergeometric solution of the BKP hierarchy with simple weight generating function. We claim that it describes a spin version of the strictly monotone…

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is…