Related papers: Mapping class group representations and Conformal …
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…
We study sequences of modular representations of the symplectic and special linear groups over finite fields obtained from the first homology of congruence subgroups of mapping class groups and automorphism groups of free groups, and the…
In this paper, we consider Galois representations of the absolute Galois group $\text{Gal}(\overline {\mathbb Q}/\mathbb Q)$ attached to modular forms for noncongruence subgroups of $\text{SL}_2(\mathbb Z)$. When the underlying modular…
We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…
We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are…
The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one particular such theory, the WZW model.…
We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL$(\bold Z)$ in terms of theta series. We apply this general setup to obtain closed and easily computable…
Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…
We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we…
We review and extend the results of [1] that gives a condition for reducibility of quantum representations of mapping class groups constructed from Reshetikhin-Turaev type topological quantum field theories based on modular categories. This…
This paper can be viewed as a continuation of [KS09] that dealt with the automorphism tower problem without Choice. Here we deal with the inequation which connects the automorphism tower and the normalizer tower without Choice and introduce…
In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.
We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition…
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and…
Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…
This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost…
Let $F$ be a number field and $p\geq7$ a rational prime. We obtain a simple descent criterion characterising those projective Galois representations $\overline\rho:G_F\to\mathrm{PGL}_2(\mathbb{F}_p)$ for which the corresponding twist…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…