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An hbar-expansion of the Toda hierarchy: a recursive construction of solutions
Kanehisa Takasaki, Takashi Takebe
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…
Thermodynamic limit of random partitions and dispersionless Toda hierarchy
Kanehisa Takasaki, Toshio Nakatsu
We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physica…
hbar-Dependent KP hierarchy
Kanehisa Takasaki, Takashi Takebe
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 oper…
Toda tau functions with quantum torus symmetries
Kanehisa Takasaki
The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of…