195 citations · 496 across the 30 of their papers we have counts for
30 papers
Polynomial tau-functions of the n-th Sawada-Kotera hierarchy
Victor Kac, Johan Van de Leur
We find all polynomial tau-functions of the n-th reduced BKP hierarchy (=n-th Sawada-Kotera hierarchy). The name comes from the fact that for n=3 the simplest equation of the hiera…
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…
Character expansion of matrix integrals
J. W. van de Leur, A. Yu. Orlov
We consider character expansion of tau functions and multiple integrals in characters of orhtogonal and symplectic groups. In particular we consider character expansions of integra…
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…
Infinite-dimensional prolongation Lie algebras and multicomponent Landau-Lifshitz systems associated with higher genus curves
S. Igonin, J. van de Leur, G. Manno +1
The Wahlquist-Estabrook prolongation method constructs for some PDEs a Lie algebra that is responsible for Lax pairs and Backlund transformations of certain type. We present some g…
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…
Irreducible Highest Weight Representations Of The Simple n-Lie Algebra
Dana Balibanu, Johan van de Leur
A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete…
Variational Lie algebroids and homological evolutionary vector fields
Arthemy V. Kiselev, Johan W. van de Leur
We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.
Givental symmetries of Frobenius manifolds and multi-component KP tau-functions
Evgeny Feigin, Johan van de Leur, Sergey Shadrin
We establish a link between two different constructions of the action of the twisted loop group on the space of Frobenius structures. The first construction (due to Givental) descr…
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…
A family of second Lie algebra structures for symmetries of dispersionless Boussinesq system
Arthemy V. Kiselev, Johan W. van de Leur
For the 3-component dispersionless Boussinesq-type system, we construct two compatible nontrivial finite deformations for the Lie algebra structure in the symmetry algebra.
Symmetry algebras of Lagrangian Liouville-type systems
Arthemy V. Kiselev, Johan W. van de Leur
The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, fo…
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…
Solutions of the WDVV Equations and Integrable Hierarchies of KP type
H. Aratyn, J. van de Leur
We show that reductions of KP hierarchies related to the loop algebra of with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dre…
Matrix integrals and the geometry of spinors
Johan van de Leur
We obtain the collection of symmetric and symplectic matrix integrals and the collection of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specif…
The construction of Frobenius manifolds from KP tau-functions
J. W. van de Leur, R. Martini
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux-Egoroff equations. This system of partial differential equations…
The geometry of spinors and the multicomponent BKP and DKP hierarchies
Victor Kac, Johan van de Leur
We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like…
An analytic description of the vector constrained KP hierarchy
G. F. Helminck, J. W. van de Leur
In this paper we give a geometric description in terms of the Grassmann manifold of Segal and Wilson, of the reduction of the KP hierarchy known as the vector -constrained KP hi…