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

Abstract

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

16 pages, submitted to a special issue of Theoretical and Mathematical Physics

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Cited by in corpus (4)

• The multicomponent 2D Toda hierarchy: Discrete flows and string equations
• Multiple sums and integrals as neutral BKP tau functions
• Symmetric polynomials, generalized Jacobi-Trudi identities and τ-functions
• Fermionic approach to the evaluation of integrals of rational symmetric functions