2011
DOI: 10.1093/imrn/rnr192
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A Class of Infinite-dimensional Frobenius Manifolds and their Submanifolds

Abstract: 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 manifolds contain finite-dimensional Frobenius submanifolds as defined on the orbit space of Coxeter groups of types B and D.

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Cited by 10 publications
(26 citation statements)
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“…This lemma can also be proved in the same way as in the appendix of [26], with the replacement ∂ z → z∂ z and dz → dz/z.…”
Section: Moreover This Multiplication Has Unitymentioning
confidence: 79%
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“…This lemma can also be proved in the same way as in the appendix of [26], with the replacement ∂ z → z∂ z and dz → dz/z.…”
Section: Moreover This Multiplication Has Unitymentioning
confidence: 79%
“…Namely, we recover the structure of Frobenius manifold M(Ã M +N −1 ; N) on the orbit space of the extended affine Weyl group W (N ) (A M +N −1 ), see [17]. Strictly speaking, N 0 does not belong to M N,M but to certain compaction of it (we remark that the abused notion "submanifold" in [26] can also be understood in this way).…”
Section: )mentioning
confidence: 99%
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“…We clarify how the hierarchy is related to the 2-component BKP and the constrained KP hierarchies. We hope that the reconstruction of the hierarchy with two types of pseudo-differential operators, as well as the study of its Hamiltonian structures, would help to cause more attention to this topic, especially its possible relation with infinite-dimensional Frobenius manifolds [6,28,29] (see also [21,23]). We will study it elsewhere.…”
Section: Discussionmentioning
confidence: 99%