Frobenius manifolds and a new class of extended affine Weyl groups ${\tilde{W}}^{(k,k+1)}(A_l)$

Abstract

We present a new class of extended affine Weyl groups ${\tilde{W}}^{(k,k+1)}(A_l)$ for $1\le k<l$ 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 ${\tilde{W}}^{(k,k+1)}(A_l)$ and also construct Landau--Ginzburg superpotentials for these Frobenius manifold structures.

36pages. Comments are welcome. arXiv admin note: text overlap with arXiv:1510.08690

Cited by in corpus (3)

• Frobenius manifolds on orbits spaces
• The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$
• Diagonal invariants and genus-zero Hurwitz Frobenius manifolds