195 citations · 496 across the 30 of their papers we have counts for
11 papers · 1 filter
Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras
Victor Kac, Johan van de Leur
This, to a large extent, expository paper, describes the theory of multicomponent hierarchies of evolution equations of XKP type, where X=A, B, C or D, and AKP=KP, and their reduct…
The generalized Giambelli formula and polynomial KP and CKP tau-functions
Victor Kac, Johan van de Leur
The first part of the paper is devoted to two descriptions of all polynomial tau-functions of the KP hierarchy: by a generalized Jacobi-Trudy formula, and a generalized Giambelli f…
BKP tau-functions as square roots of KP tau-functions
Johan van de Leur
It is well-known that a BKP tau-function is the square root of a certain KP tau-function, provided one puts the even KP times equal to zero. In this paper we compute for all polyno…
p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p)
Sylvain Carpentier, Alberto De Sole, Victor G. Kac +2
For each partition p of an integer N \geq 2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present…
Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
Victor Kac, Johan van de Leur
We give 4 formulations of the Modified KP hierarchy and show that they are equivalent. We also discuss the reductions of the MKP hierarchy to the modified -KdV hierarchies. As a…
On rational R-matrices with adjoint SU(n) symmetry
Laurens Stronks, Johan van de Leur, Dirk Schuricht
Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) sp…
Pfaffian and determinantal tau functions I
J. W. van de Leur, A. Yu. Orlov
Adler, Shiota and van Moerbeke observed that a tau function of the Pfaff lattice is a square root of a tau function of the Toda lattice hierarchy of Ueno and Takasaki. In this pape…
The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
Johan van de Leur
The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector f…
Multiple sums and integrals as neutral BKP tau functions
J. Harnad, J. W. van de Leur, A. Yu. Orlov
We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Sch…
Involutive distributions of operator-valued evolutionary vector fields and their affine geometry. II
Arthemy V. Kiselev, Johan W. van de Leur
We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra o…
Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach
H. Aratyn, J. van de Leur
We present an explicit method to perform similarity reduction of a Riemann-Hilbert factorization problem for a homogeneous GL (N, C) loop group and use our results to find solution…