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We use a Grassmannian framework to define multi-component tau functions asexpectation values of certain multi-component Fermi operators satisfying simplebilinear commutation relations on Clifford algebra. The tau functions containboth positive and negative flows and are shown to satisfy the $2n$-component KPhierarchy. The hierarchy equations can be formulated in terms ofpseudo-differential equations for $n \times n$ matrix wave functions derived interms of tau functions. These equations are cast in form of Sato-Wilsonrelations. A reduction process leads to the AKNS, two-component Camassa-Holmand Cecotti-Vafa models and the formalism provides simple formulas for theirsolutions

Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows