We construct a class of infinite-dimensional Frobenius manifolds on the spaceof pairs of certain even functions meromorphic inside or outside the unitcircle. Via a bi-Hamiltonian recursion relation, the principal hierarchiesassociated to such Frobenius manifolds are found to be certain extensions ofthe dispersionless two-component BKP hierarchy. Moreover, we show that theseinfinite-dimensional Frobenius manifolds contain finite-dimensional Frobeniussubmanifolds as defined on the orbit space of Coxeter groups of types B and D.
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