Related papers: Conformal Characters and Theta Series

An analytic representation with Theta functions on a torus, for systems with variables in Z(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is…

We study some explicit Siegel modular forms from Weil representations. For the classical theta group $\Gamma_m(1,2)$ with $m > 1$, there are some eighth roots of unity associated with these modular forms, as noted in the works of Andrianov,…

The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals.…

For positive integer p=k+2, we construct a logarithmic extension of the ^sl(2)_k conformal field theory of integrable representations by taking the kernel of two fermionic screening operators in a three-boson realization of ^sl(2)_k. The…

A formula is presented for the modular transformation matrix S for any simple current extension of the chiral algebra of a conformal field theory. This provides in particular an algorithm for resolving arbitrary simple current fixed points,…

In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in his book[p.189, Tata…

Let $\f$ be a primitive, cuspidal Hilbert modular form of parallel weight. We investigate the Rankin convolution $L$-values $L(\f,\g,s)$, where $\g$ is a theta-lift modular form corresponding to a finite-order character. We prove weak forms…

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid…

Using the representation theory of the subgroups SL_2(Z_p) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to 'good' fusion algebras. Furthermore, the…

$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…

We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an…

We analyze certain characters of vertex algebras that can be expressed using (generalized) q-MZVs. We consider: (i) characters of vertex algebras associated to arc spaces, (ii) characters (or indices) of $\mathcal{S}$-class vertex operator…

This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…

We discuss the modular invariance of the SL(2,R) WZW model. In particular, we discuss in detail the modular invariants using the \hat{sl}(2,R) characters based on the discrete unitary series of the SL(2,R) representations. The explicit…

We review recent developments in the context of two-dimensional conformally invariant sigma-models. These quantum field theories play a prominent role in the covariant superstring quantization in flux backgrounds and in the analysis of…

It is shown that every weak Jacobi form of weight zero and index one on a congruence subgroup of the full Jacobi group can be decomposed into $N=4$ superconformal characters. Additionally, a simple expression for the mock modular form…

We introduce and study higher depth quantum modular forms. We construct two families of examples coming from rank two false theta functions, whose "companions" in the lower half-plane can be also realized both as double Eichler integrals…

We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings…

We discuss certain representations of GL 2 Fq[T] in equal characteristic and associated vectorial modular forms

We discuss some properties of the tower of mapping class group representations associated to a Rational Conformal Field Theory. In particular, after reviewing the elementary properties of the modular representation, we discuss the Galois…