相关论文: Modular invariants and their fusion rules

We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing "invariant versions" of iterated integrals of modular forms. The construction will be based on an extension of…

An invariant of a model of genus one curve is a polynomial in the coefficients of the model that is stable under certain linear transformations. The classical example of an invariant is the discriminant, which characterizes the singularity…

We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…

The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In…

The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…

We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.

We determine the fusion rules of the equivariantization of a fusion category $\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\mathcal{C}$ and group-theoretical data associated to the group action. As an…

The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.

We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine…

This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicalities aside. We focus on relations among…

For any finite group G with a finite G-set X and a modular tensor category C we construct a part of the algebraic structure of an associated G-equivariant monoidal category: For any group element g in G we exhibit the module category…

The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…

In this paper, we extend the notion of modular functor and fusion category to what we called $G$ equivariant modular functor and $G$ equivariant fusion category, where $G$ is a finite group, and establish a correspondence between between…

We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…

We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.

Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or…

We study some conformally invariant integral equations using the method of moving spheres.

We introduce two new sets of invariant functions of quark mass matrices, which express the constraints on these mass matrices due to knowledge of the quark mixing matrix. These invariants provide a very simple method to test candidate forms…

The problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.

Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…