相关论文: Categorical representations of categorical groups

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…

Let $c$ be the family of irreducible representations of a Weyl group $W$ corresponding to a two-sided cell of $W$. We define a subset $A_c$ of $c$ which contains the special representation of $W$ in $c$ and is in canonical bijection with…

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.

Complex classical Cayley-Klein categories ${\bf A({\bj})}$, ${\bf B({\bj})}$, ${\bf C({\bj})}$ and ${\bf D({\bj})}$ are constructed by the method of categorical extension of the complex classical Cayley-Klein groups $SL(2n;{\bj};{\Bbb C}),…

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…

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…

In this work, we analyze the structure of the category of partial representations of a finite group $G$ as a multifusion category, providing an alternative way to describe simple objects and their tensor products. We describe the…

We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…

The monoidal category of Soergel bimodules is an incarnation of the Hecke category, a fundamental object in representation theory. We present this category by generators and relations, using the language of planar diagrammatics. We show…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical…

We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…

We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.

A $\mathcal{C}$-set is a functor from the category $\mathcal{C}$ to the category of finite sets and functions. The category of $\mathcal{C}$-sets, $\mathcal{C} - \operatorname*{set}$, is defined as the category whose objects are…