Related papers: The Image of Functor Morphing

We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…

Motivated by the human way of memorizing images we introduce their functional representation, where an image is represented by a neural network. For this purpose, we construct a hypernetwork which takes an image and returns weights to the…

For every quiver (valued) of finite representation type we define a finitely presented group called a picture group. This group is very closely related to the cluster theory of the quiver. For example, positive expressions for the Coxeter…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.

We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that…

Let F be a local field of positive characteristic, and let G be either a Heisenberg group over F, or a certain (nonabelian) two-dimensional unipotent group over F. If H is an arithmetic subgroup of G, we provide an explicit description of…

We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

This paper is an exploration of the faithful transitive permutation representations of the orientation-preserving automorphisms groups of highly symmetric toroidal maps and hypermaps. The main theorems of this paper give a list of all…

The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…

We prove the functoriality for proper push-forward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support…

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…

We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…