Related papers: Dicyclic groups and Frobenius manifolds

The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an…

We show that bi-flat $F$-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter…

Generalizing a construction presented in [3], we show that the orbit space of $B_2$ less the image of coordinate lines under the quotient map is equipped with two Dubrovin-Frobenius manifold structures which are related respectively to the…

From any given Frobenius manifold one may construct a so-called dual structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying…

The work proves that, for three-dimensional upper triangular groups over a field of odd characteristic with an abelian unipotent subgroup, the ring of invariants is polynomial if and only if the unipotent subgroup is generated by…

Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

In this paper we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps. In particular, a few classical results of Steinberg and Deligne & Lusztig on complex representations of finite…

The geometric Frobenius morphism on smooth varieties is an fppf-fiber bundle. We study representations of the structure group scheme. In particular, we describe irreducible representations and compute its Grothendieck ring of finite…

We reformulate Dubrovin's almost duality of Frobenius structures to Saito structures without metric. Then we formulate and study the existence and uniqueness problem of the natural Saito structure on the orbit spaces of finite complex…

It is proved that the orbit space of an irreducible representation of a simple connected compact Lie group of type B, C, or D can be a smooth manifold only in two cases.

We define certain extensions of Jacobi groups of $A_n$, prove an analogue of Chevalley Theorem for their invariants, and construct a Dubrovin Frobenius structure on it orbit space.

We construct a new local Poisson bracket compatible with the second unconstrained Adler-Gelfand-Dickey bracket. The resulting bihamiltonian structure admits a dispersionless limit and the leading term defines a logarithmic…

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…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

Two classical rings of invariants are shown to be Frobenius split: for the special linear group acting on the direct sum of several copies of the defining representation and several copies of the dual of the defining representation; and for…

We define certain extensions of Jacobi groups of $A_1$, prove an analogue of Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.

We prove that the quotient of an irreducible representation of a special unitary group of rank greater than 1 cannot be a smooth manifold.

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…