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Earlier we explained that partition functions of various matrix models can beconstructed from that of the cubic Kontsevich model, which, therefore, becomesa basic elementary building block in "M-theory" of matrix models. However, theless topical complex matrix model appeared to be an exception: itsdecomposition involved not only the Kontsevich tau-function but also anotherconstituent, which we now identify as the Brezin-Gross-Witten (BGW) partitionfunction. The BGW tau-function can be represented either as a generatingfunction of all unitary-matrix integrals or as a Kontsevich-Penner model withpotential 1/X (instead of X^3 in the cubic Kontsevich model).

BGWM as Second Constituent of Complex Matrix Model