A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds

Details A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds

2011-03-21

arxiv.org/abs/1103.4048v2

Physics

Mathematical Physics

35 pages. Some errors are corrected. To appear in IMRN

Scientific paper

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.

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