Related papers: Bilinear Expansions of KP Multipair Correlators in…

Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations…

The Schur function expansion of Sato-Segal-Wilson KP tau-functions is reviewed. The case of tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Pl\"ucker coordinate coefficients…

We prove that multiparameter Schur $Q$-functions, which include as specializations factorial Schur $Q$-functions and classical Schur $Q$-functions, provide solutions of the BKP hierarchy

We study the series expansion of the tau function of the BKP hierarchy applying the addition formulae of the BKP hierarchy. Any formal power series can be expanded in terms of Schur functions. It is known that, under the condition…

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…

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

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,…

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 introduce hypergeometric functions related to projective Schur functions $Q_{\lambda}$ and describe their properties. Linear equations, integral representations and Pfaffian representations are obtained. These hypergeometric functions…

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 their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar conjecture for the Br\'ezin-Gross-Witten…

We derive a formula for the connected $n$-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou in [arXiv:1507.01679]. Moreover, we…

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…

We introduce a useful and rather simple classes of BKP tau functions which which we shall shall call "easy tau functions". We consider the "large BKP hiearchy" related to $O(2\infty +1)$ which was introduced in \cite{KvdLbispec} (which is…

I present a set of remarks related to joint works \cite{paper1},\cite{paper2},\cite{paper3},\cite{MMNO}. These are remarks about polynomials solutions and vertex operators, eigenproblem for polynomials and a remark related to the the…

We introduce a useful and rather simple class of BKP tau functions which which we shall call "easy tau functions". We consider two versions of BKP hierarchy, one we will call "small BKP hierarchy" (sBKP) related to $O(\infty)$ introduced in…

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…

We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simple form when written in terms of some notation based on the…

We derive a bilinear expansion expressing elements of a lattice of KP $\tau$-functions, labelled by partitions, as a sum over products of pairs of elements of an associated lattice of BKP $\tau$-functions, labelled by strict partitions.…

We consider a special class of solutions of the BKP hierarchy which we call $\tau$-functions of hypergeometric type. These are series in Schur $Q$-functions over partitions, with coefficients parameterised by a function of one variable…