相关论文: Multiplying Modular Forms
This article is devoted to branching problems for holomorphic discrete series representations of a conformal group $G$ of a tube domain $T_Omega$ over a symmetric cone $\Omega$. More precisely, we analyse restrictions of such…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrodinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the…
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…
We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we…
We study branching multiplicity spaces of complex classical groups in terms of GL(2) representations. In particular, we show how combinatorics of GL(2) representations are intertwined to make branching rules under the restriction of GL(n)…
An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show…
The aim of this note is to prove various general properties of a generalization of the full module of first order differential operators on a commutative ring - a $\operatorname{D}$-Lie algebra. A $\operatorname{D}$-Lie algebra $\tilde{L}$…
We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
The goal of this article is to study the branching problem for a holomorphic discrete series representation of the conformal group of a simple Euclidean Jordan algebra $V$ restricted to the subgroup…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
Spinor structure is understood as a totality of tensor products of biquaternion algebras, and the each tensor product is associated with an irreducible representation of the Lorentz group. A so-defined algebraic structure allows one to…
We prove existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to…
Inspired by Borcherds' questions, Guerzhoy constructed a new type of Hecke operators $\mathcal{T}(p)$, called the multiplicative Hecke operators, which acts on the space of meromorphic modular forms on the full modular group ${\rm SL}(\Z)$.…
We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these…