Related papers: Dicyclic groups and Frobenius manifolds

The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…

We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy being that this should force the group to be, in some sense,…

We study regular non-semisimple Dubrovin-Frobenius manifolds in dimensions 2,3,4. We focus on the case where the Jordan canonical form of the operator of multiplication by the Euler vector field has a single Jordan block. Our results rely…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

Let $F$ be a $p$-adic field. Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the groups $\{GL_n(F)\}_{n=0}^\infty$ taken together, with multiplication defined in the sense of parabolic…

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…

Starting from the Weierstrass elliptic function, we study the associated Frobenius structure, incorporating the perspective of derived categories, particularly that of homological mirror symmetry. Given a deformation of the Weierstrass…

For any finite abelian group G, we study the moduli space of abelian $G$-covers of elliptic curves, in particular identifying the irreducible components of the moduli space. We prove that, in the totally ramified case, the moduli space has…

We give a uniform, Lie-theoretic mirror symmetry construction for the Frobenius manifolds defined by Dubrovin-Zhang in arXiv:hep-th/9611200 on the orbit spaces of extended affine Weyl groups, including exceptional Dynkin types. The B-model…

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

We determine the unipotent orbits attached to degenerate Eisenstein series on general linear groups. This confirms a conjecture of David Ginzburg. This also shows that any unipotent orbit of general linear groups does occur as the unipotent…

Any sufficiently often differentiable curve in the orbit space $V/G$ of a real finite-dimensional orthogonal representation $G \to O(V)$ of a finite group $G$ admits a differentiable lift into the representation space $V$ with locally…

We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield F of "max-plus…

We construct Frobenius structures of "dual type" on the moduli space of ramified coverings of $\mathbb{P}^1$ with given ramification type over two points, generalizing a construction of Dubrovin. A complete hierarchy of hydrodynamic type is…

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius…

To every finite-dimensional $\mathbb C$-algebra $\Lambda$ of finite representation type we associate an affine variety. These varieties are a large generalization of the varieties defined by "$u$ variables" satisfying "$u$-equations", first…

This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…

In this paper we introduce a new invariant for the action of a finite group $G$ on a compact complex curve of genus $g$. With the aid of this invariant we achieve the classification of the components of the moduli space of curves with an…

Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide polynomial Frobenius manifolds. Flat coordinates of the Frobenius metric $\eta$ are Saito polynomials which are distinguished basic invariants of the…

This paper is a continuation and elaboration of our work quant-ph/0206057 (Nucl. Phys. B, 1968, 7, 79) where some approach to the variable-mass problem were proposed. Here we have found a concret realization of irreducible representations…