Progr. Math. 237(Infinite dimensional algebras and quantum integrable systems) 205-224 Dec 2005 [Refereed]
The sheaves of conformal blocks and conformal coinvariants of the twisted WZW
model have a factorisation property and are locally free even at the boundary
of the moduli space, where the elliptic KZ equations and the Baxter-Belavin
elliptic r matrix degenerate to the trigonometric KZ equations and the
trigonometric r matrix,o respectively. Etingof's construction of the elliptic
KZ equations is ...
J. Phys. A: Math. Theor. 43(32) 325205-(22p.) Jul 2010 [Refereed]
The notion of non-degenerate solutions for the dispersionless Toda hierarchy
is generalized to the universal Whitham hierarchy of genus zero with
marked points. These solutions are characterized by a Riemann-Hilbert problem
(generalized string equations) with respect to two-dimensional canonical
transformations, and may be thought of as a kind of general solutions of the
hierarchy. The Ri...
The \hbar-dependent KP hierarchy is a formulation of the KP hierarchy that
depends on the Planck constant \hbar and reduces to the dispersionless KP
hierarchy as \hbar -> 0. A recursive construction of its solutions on the basis
of a Riemann-Hilbert problem for the pair (L,M) of Lax and Orlov-Schulman
operators is presented. The Riemann-Hilbert problem is converted to a set of
recursion relatio...
Int.J.Mod.Phys. A 19(S2 (Conformal Field Theory and Integrable Models)) 418-435 2004 [Refereed]
Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is
described by the degeneration of the twisted WZW model on elliptic curves. The
spaces of conformal blocks and conformal coinvariants of the degenerate model
are factorised into those of the orbifold WZW model.
We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on
elliptic curves at the critical level. Bethe eigenvectors are obtained by the
bosonisation technique.
A construction of general solutions of the \hbar-dependent Toda hierarchy is
presented. The construction is based on a Riemann-Hilbert problem for the pairs
(L,M) and (\bar L,\bar M) of Lax and Orlov-Schulman operators. This
Riemann-Hilbert problem is translated to the language of the dressing operators
W and \bar W. The dressing operators are set in an exponential form as W =
e^{X/\hbar} and \...
This is a summary of a recursive construction of solutions of the
hbar-dependent KP hierarchy. We give recursion relations for the coefficients
X_n of an hbar-expansion of the operator X = X_0 + \hbar X_1 + \hbar^2 X_2 +
... for which the dressing operator W is expressed in the exponential form W =
\exp(X/\hbar). The asymptotic behaviours of (the logarithm of) the wave
function and the tau func...
It has been shown that the dispersionless KP hierarchy (or the Benney
hierarchy) is reduced to the chordal Löwner equation. We show that the radial
Löwner equation also gives reduction of a dispersionless type integrable
system. The resulting system acquires another degree of freedom and becomes the
dcmKP hierarchy, which is a ``half'' of the dispersionless Toda hierarchy. The
results of th...
