相关论文: Representation and character theory in 2-categorie…

Identifiable causal representation learning seeks to uncover the true causal relationships underlying a data generation process. In medical imaging, this presents opportunities to improve the generalisability and robustness of task-specific…

The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…

A group is called capable if it is a central factor group. We characterize the capable 2-generator 2-groups of class 2 in terms of a standard presentation.

We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…

We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…

We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…

In this note we clarify the relevance of ``connections up to homotopy'' to the theory of characteristic classes. We have already remarked \cite{Crai} that such connections up to homotopy can be used to compute the classical Chern…

This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System C. For propositional…

We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is…

In [Frobenius1896] it was shown that many important properties of a finite group could be examined using formulas involving the character ratios of group elements, i.e., the trace of the element acting in a given irreducible representation,…

We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…

The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…

We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters…

In this article, we define and study the class of simple transitive $2$-representations of finitary $2$-categories. We prove a weak version of the classical Jordan-H\"older Theorem where the weak composition subquotients are given by simple…

Bernstein blocks of complex representations of p-adic reductive groups have been computed in a large amount of examples, in part thanks to the theory of types a la Bushnell and Kutzko. The output of these purely representation-theoretic…

In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple…

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite…

It is well-known that the representation theory of the finite group of unipotent upper-triangular matrices $U_n$ over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one…

Two groups are called isocategorical over a field $k$ if their respective categories of $k$-linear representations are monoidally equivalent. We classify isocategorical groups over arbitrary fields, extending the earlier classification of…

We develop a unified representation theory for the categories of finite subsets and relation-preserving maps of highly homogeneous relational structures classified by Cameron. For any commutative coefficient ring $k$, we extend the…