The geometry of spinors and the multicomponent BKP and DKP hierarchies
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 KdV, NLS, AKNS or…
The n-Component KP Hierarchy and Representation Theory
It is the aim of the present article to give all formulations of the n-component KP hierarchy and clarify connections between them. The generalization to the n-component KP hierarchy is important…
CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school (Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806{ 3812) (see also (Kac V.G., van de Leur…
Matrix Integrals and the Geometry of Spinors
- J. Leur
- Physics
- 29 September 1999
Abstract 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 specific…
Bosonic and Fermionic Realizations of The Affine Algebra sˆo2n
We give an explicit description of the Kac-Peterson-Lepowsky constr tion of the basic representation for the affine Lie algebra sˆo2n(C). Using the conjugacy classes of the Weyl group of sˆo2n(C), we…
Bosonic and fermionic realizations of the affine algebra $$g\hat l_n $$
AbstractWe give an explicit description of all inequivalent Heisenberg subalgebras of the affine Lie algebra
$$g\hat l_n (\mathbb{C})$$
and the associated vertex operator constructions of the level…
Twisted GLn Loop Group Orbit and Solutions of the WDVV Equations
- J. Leur
- Mathematics
- 12 April 2000
We show that all (n-component) KP tau-functions, which are related to the twisted loop group of GLn, give solutions of the Darboux-Egoroff system of PDE’s. Using the Geometry of the Grassmannian we…
Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP1?> orbifolds
- Guido Carlet, J. Leur
- Mathematics
- 5 April 2013
We prove that the Hirota quadratic equations of Milanov and Tseng define an integrable hierarchy which is equivalent to the extended bigraded Toda hierarchy (EBTH). In particular this confirms a…
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