Related papers: Congruence subgroups and rational conformal field …

A work of Sorensen is rewritten here to include nontrivial types at the infinite places. This extends results of K. Ribet and R. Taylor on level-raising for algebraic modular forms on D^{\times}, where D is a definite quaternion algebra…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

In this article we study the combinatorics of congruence subgroups of the modular group. We consider the notion of minimal monomial solutions. These are the solutions of a matrix equation (also appearing in the study of Coxeter friezes),…

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

We study modularity of the characters of a vertex (super)algebra equipped with a family of conformal structures. Along the way we introduce the notions of rationality and cofiniteness relative to such a family. We apply the results to…

We calculate characters and supercharacters for irreducible, admissible representations of the affine superalgebra sl(2|1) in both the Ramond and Neveu-Schwarz sectors and discuss their modular properties in the special case of level…

Let $F$ be a non-Archimedean local field and let $G$ be the general linear group $G = \text{\rm GL}_n(F)$. Let $\theta_1$, $\theta_2$ be simple characters in $G$. We show that $\theta_1$ intertwines with $\theta_2$ if and only if $\theta_1$…

The graded parafermion conformal field theory at level k is a close cousin of the much-studied Z_k parafermion model. Three character formulas for the graded parafermion theory are presented, one bosonic, one fermionic (both previously…

Possible short and semi-short positive energy, unitary representations of the Osp(2N|4) superconformal group in three dimensions are discussed. Corresponding character formulae are obtained, consistent with character formulae for the…

We explore higher-dimensional conformal field theories (CFTs) in the presence of a conformal defect that itself hosts another sub-dimensional defect. We refer to this new kind of conformal defect as the composite defect. We elaborate on the…

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…

Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under…

In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N=2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure…

If R, S, T are irreducible SL_3-representations, we give an easy and explicit description of a basis of the space of equivariant maps from R tensor S to T. We apply this method to the rationality problem for invariant function fields. In…

For a fixed integer $t \geq 2$, we consider the irreducible characters of representations of the classical groups of types A, B, C and D, namely $\text{GL}_{tn}, \text{SO}_{2tn+1}, \text{Sp}_{2tn}$ and $\text{O}_{2tn}$, evaluated at…

Let $\Gamma$ be an irreducible lattice in a semisimple Lie group of real rank at least $2$. Suppose that $\Gamma$ has property (T;FD), that is, its finite dimensional representations have a uniform spectral gap. We show that if $\Gamma$ is…

False theta functions form a family of functions with intriguing modular properties and connections to mock modular forms. In this paper, we take the first step towards investigating modular transformations of higher rank false theta…

Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…

We find some modularity criterion for a product of Klein forms of the congruence subgroup $\Gamma_1(N)$ and, as its application, construct a basis of the space of modular forms for $\Gamma_1(13)$ of weight $2$. In the process we face with…

For positive integers $u$ and $v$, let $L_u=\begin{bmatrix} 1 & 0 \\ u & 1 \end{bmatrix}$ and $R_v=\begin{bmatrix} 1 & v \\ 0 & 1 \end{bmatrix}$. Let $S_{u,v}$ be the monoid generated by $L_u$ and $R_v$, and $G_{u,v}$ be the group generated…