Related papers: Holographic Equidistribution
We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate…
We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…
The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…
We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom up…
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 extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…
For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…
Symmetric functions appear in many areas of mathematics and physics, including enumerative combinatorics, the representation theory of symmetric groups, statistical mechanics, and the quantum statistics of ideal gases. In the commutative…
Recently, Harvey and Wu proposed a suitable Hecke operator for vector-valued $SL(2,\mathbb{Z})$ modular forms to connect the characters of different 2d rational conformal field theories (RCFTs). We generalize such an operator to the 2d…
Given a Hecke symmetry $R$, one can define a matrix bialgebra $E_R$ and a matrix Hopf algebra $H_R$, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to $R$. We show that for an even…
Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically…
We compute generators and relations for a certain $2$-adic Hecke algebra of level $8$ associated with the double cover of $\mathrm{SL}_2$ and a $2$-adic Hecke algebra of level $4$ associated with $\mathrm{PGL}_2$. We show that these two…
Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…
Affine Hecke algebras arise naturally in the study of smooth representations of reductive $p$-adic groups. Finite dimensional complex representations of affine Hecke algebras (under some restriction on the isogeny class and the parameter…
In this paper, we study the holographic descriptions of the conformal block of heavy operators in two-dimensional large c conformal field theory. We consider the case that the operators are pairwise inserted such that the distance between…
In this study, we introduce the theory of what we call Hecke vector-forms. A Hecke vector-form can be viewed as a vector function representation of some quasiautomorphic form that transforms like an automorphic form on an arbitrarily chosen…
We show how there is a natural action on the cohomology groups attached to certain subgroups of GL_n(F) of the Hecke operators defined as elements in an adelic double coset algebra. Our main result is, that if a system of eigenvalues for…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…