Ian A. B. Strachan
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View article: Dubrovin duality and mirror symmetry for ADE resolutions
Dubrovin duality and mirror symmetry for ADE resolutions Open
We show that, under Dubrovin’s notion of ‘almost’ duality, the Frobenius manifold structure on the orbit spaces of the extended affine Weyl groups of type is dual, for suitable choices of weight markings, to the equivariant quantum coho…
View article: Dubrovin duality and mirror symmetry for ADE resolutions
Dubrovin duality and mirror symmetry for ADE resolutions Open
We show that, under Dubrovin's notion of ''almost'' duality, the Frobenius manifold structure on the orbit spaces of the extended affine Weyl groups of type $\mathrm{ADE}$ is dual, for suitable choices of weight markings, to the equivarian…
View article: Diagonal invariants and genus-zero Hurwitz Frobenius manifolds
Diagonal invariants and genus-zero Hurwitz Frobenius manifolds Open
The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While s…
View article: Legendre transforms for type A<sub>n</sub> and B<sub>n</sub> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> </mml:math> -systems
Legendre transforms for type A<sub>n</sub> and B<sub>n</sub> -systems Open
The Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations have a rich structure related to the theory of Frobenius manifolds, with many known families of solutions. A Legendre transformation is a symmetry of the WDVV equations, introduced by…
View article: Regular F-manifolds with eventual identities
Regular F-manifolds with eventual identities Open
Given an F -manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity, the definition of which ensures that the dual object is a…
View article: Legendre transforms for type $A_{n}$ and $B_{n}$ $\vee$-systems
Legendre transforms for type $A_{n}$ and $B_{n}$ $\vee$-systems Open
The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations have a rich structure related to the theory of Frobenius manifolds, with many known families of solutions. A Legendre transformation is a symmetry of the WDVV equations, introduced by…
View article: Regular F -manifolds with eventual identities
Regular F -manifolds with eventual identities Open
Given an F-manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity, the definition of which ensure that the dual object is als…
View article: Remarkable botanical records from Corrour in Westerness (v.c.97), including Baldellia repens (Alismataceae) and Illecebrum verticillatum (Caryophyllaceae), new to Scotland
Remarkable botanical records from Corrour in Westerness (v.c.97), including Baldellia repens (Alismataceae) and Illecebrum verticillatum (Caryophyllaceae), new to Scotland Open
Biological recording in Britain has increased in accessibility and popularity due to recent technological advances. However, remote locations may still be under-recorded, particularly for aquatic plants and taxonomically challenging groups…
View article: Extended ⋁-systems and trigonometric solutions to the WDVV equations
Extended ⋁-systems and trigonometric solutions to the WDVV equations Open
Rational solutions of the Witten–Dijkgraaf–Verlinde–Verlinde (or WDVV) equations of associativity are given in terms of configurations of vectors, which satisfy certain algebraic conditions known as ⋁-conditions [A. P. Veselov, Phys. Lett.…
View article: The Saito determinant for Coxeter discriminant strata
The Saito determinant for Coxeter discriminant strata Open
Let $W$ be a finite Coxeter group and $V$ its reflection representation. The orbit space $\mathcal{M}_W= V/W$ has the remarkable Saito flat metric defined as a Lie derivative of the $W$-invariant bilinear form $g$. We find determinant of t…
View article: Extended affine Weyl groups of BCD-type: Their Frobenius manifolds and Landau–Ginzburg superpotentials
Extended affine Weyl groups of BCD-type: Their Frobenius manifolds and Landau–Ginzburg superpotentials Open
View article: A construction of Multidimensional Dubrovin-Novikov Brackets
A construction of Multidimensional Dubrovin-Novikov Brackets Open
A method for the construction of classes of examples of multi-dimensional, multi-component Dubrovin-Novikov brackets of hydrodynamic type is given. This is based on an extension of the original construction of Gelfand and Dorfman which gav…
View article: Darboux coordinates for Hamiltonian structures defined by Novikov algebras
Darboux coordinates for Hamiltonian structures defined by Novikov algebras Open
The Gauss-Manin equations are solved for a class of flat-metrics defined by Novikov algebras, this generalizing a result of Balinskii and Novikov who solved this problem in the case of commutative Novikov algebras (where the algebraic cond…
View article: Extended V-systems and almost-duality for extended affine Weyl orbit spaces
Extended V-systems and almost-duality for extended affine Weyl orbit spaces Open
Rational solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations of associativity are given in terms a configurations of vectors which satisfy certain algebraic conditions known as $\bigvee$-conditions. The simplest example…
View article: Extended V-systems and almost-duality for extended affine Weyl orbit\n spaces
Extended V-systems and almost-duality for extended affine Weyl orbit\n spaces Open
Rational solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV)\nequations of associativity are given in terms a configurations of vectors which\nsatisfy certain algebraic conditions known as $\\bigvee$-conditions. The\nsimplest exa…
View article: Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy
Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy Open
We introduce a Frobenius algebra-valued Kadomtsev-Petviashvili (KP) hierarchy and show the existence of Frobenius algebra-valued τ-function for this hierarchy. In addition, we construct its Hamiltonian structures by using the Adler-Dickey-…