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Frobenius manifolds and a new class of extended affine Weyl groups $\widetilde{W}^{(k,k+1)}(A_l)$
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abstract
We present a new class of extended affine Weyl groups $\widetilde{W}^{(k,k+1)}(A_l)$ for $1\leq k <l$ and obtain an analogue of Chevalley-type theorem for their invariants. We further show the existence of Frobenius manifold structures on the orbit spaces of $\widetilde{W}^{(k,k+1)}(A_l)$ and also construct Landau--Ginzburg superpotentials for these Frobenius manifold structures.
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Cited by 1 Pith paper
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Rank shift conditions and reductions of 2d-Toda theory
Imposing rank-one and rank-two shift conditions on symmetric and skew-symmetric moment matrices yields the C-Toda and B-Toda hierarchies with explicit Lax matrices, and shows the Pfaff lattice is the large BKP hierarchy.
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