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We use $p$-component fermions $(p=2,3,...)$ to present $(2p-2)N$-foldintegrals as a fermionic expectation value. This yields fermionicrepresentation for various $(2p-2)$-matrix models. Links with the $p$-componentKP hierarchy and also with the $p$-component TL hierarchy are discussed. Weshow that the set of all (but two) flows of $p$-component TL changes standardmatrix models to new ones.

Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy