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We establish a link between two different constructions of the action of thetwisted loop group on the space of Frobenius structures. The first construction(due to Givental) describes the action of the twisted loop group on thepartition functions of formal Gromov-Witten theories. The explicit formulas forthe corresponding tangent action were computed by Y.-P. Lee. The secondconstruction (due to van de Leur) describes the action of the same group on thespace of Frobenius structures via the multi-component KP hierarchies. Our maintheorem states that the genus zero restriction of the Y.-P. Lee formulascoincides with the tangent van de Leur action.

Givental symmetries of Frobenius manifolds and multi-component KP tau-functions