Geodesic
Fermionic construction of the~partition function for multimatrix models and the~multicomponent Toda lattice hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 265-277

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We use $p$-component fermions, $p=2,3,\dots$, to represent $(2p-2)N$-fold integrals as a fermionic vacuum expectation. This yields a fermionic representation for various $(2p-2)$-matrix models. We discuss links with the $p$-component Kadomtsev–Petviashvili hierarchy and also with the $p$-component Toda lattice hierarchy. We show that the set of all but two flows of the $p$-component Toda lattice hierarchy changes standard matrix models to new ones.
Keywords: matrix model, tau function of multicomponent Toda chain, integrable system. 
@article{TMF_2007_152_2_a4,
     author = {J. Harnad and A. Yu. Orlov},
     title = {Fermionic construction of the~partition function for multimatrix models and the~multicomponent {Toda} lattice hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {265--277},
     publisher = {mathdoc},
     volume = {152},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a4/}
}
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J. Harnad; A. Yu. Orlov. Fermionic construction of the~partition function for multimatrix models and the~multicomponent Toda lattice hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 265-277. http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a4/