A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds

Int. Math. Res. Not. 2012, no. 19, 4520--4562 We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to such Frobenius manifolds are found to be certain extensions of the dispersionless two-component BKP hierarchy. Moreover, we show that these infinite-dimensional Frobenius manifolds contain finite-dimensional Frobenius submanifolds as defined on the orbit space of Coxeter groups of types B and D.