Related papers: Linear dimension of group actions

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…

We study the representations of the commutator subgroup of the braid group with n strands in the symmetric group of degree r. Motivated by some experimental results, we conjecture that for n>r, every such representation is trivial.

In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…

The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…

This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…

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…

The action dimension of a discrete group $G$ is the minimum dimension of contractible manifold that admits a proper $G$-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of…

The purpose of this note is to extend the classical Aschbacher--O'Nan--Scott theorem for finite groups to the class of countable linear groups. This relies on the analysis of primitive actions carried out in a previous paper. Unlike the…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. Balmer and Gallauer's recent result on finite $p$-permutation resolutions of $kG$-modules motivates the study of an intriguing new invariant; the $p$-permutation…

We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…

We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to…

The problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right…

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector…

In the recent paper [A14], a geometric realization to minimal representations of simple real Lie groups of non Hermitian type is given, based on the geometric setting introduced in [A11]. We give in this paper a geometric realization to…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…

A permutation polytope is the convex hull of a group of permutation matrices. In this paper we investigate the combinatorics of permutation polytopes and their faces. As applications we completely classify permutation polytopes in…