Related papers: Factorized Combinations of Virasoro Characters

Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles. It is shown that the transition to the Hamiltonian formalism leads to the…

It is well-known that the representation theory of the finite group of unipotent upper-triangular matrices $U_n$ over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one…

We obtain a general characterization of discrete-time all-pass rational matrix functions from state-space representations. It can be employed to address model reduction problems in the same vein of the theory developed by Glover in the…

We give a classification of all quasitriangular structures and ribbon elements of $\mathcal{D}(G)$ explicitly in terms of group homomorphisms and central subgroups. This can equivalently be interpreted as an explicit description of all…

We study asymptotics of reducible representations of the symmetric groups S_q for large q. We decompose such a representation as a sum of irreducible components (or, alternatively, Young diagrams) and we ask what is the character of a…

G. Andrews proved that if $n$ is a prime number then the coefficients $a_k$ and $a_{k+n}$ of the product $(q,q)_\infty/(q^n,q^n)_\infty=\sum_k a_kq^k$ have the same sign, see [A1]. We generalize this result in several directions. Our…

In this article we present a neural network based model to emulate matrix elements. This model improves on existing methods by taking advantage of the known factorisation properties of matrix elements. In so doing we can control the…

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $\hat w$-operators. In this letter, we demonstrate that…

We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form $z' = H(z,\varepsilon)$, $z\in\mathbb{R}^n$ and $\varepsilon\ll 1$. Our main result is the derivation of computable,…

AGT correspondence gives an explicit expressions for the conformal blocks of $d=2$ conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the…

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

We consider $\alpha$-heavy conformal operators in CFT$_2$ which dimensions grow as $h = O(c^\alpha)$ with $\alpha$ being non-negative rational number and conjecture that the large-$c$ asymptotics of the respective 4-point Virasoro conformal…

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…

We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of…

Using the properties of the local Boltzmann weights of integrable interaction-round-a-face (IRF or face) models we express local operators in terms of generalized transfer matrices. This allows for the derivation of discrete functional…

We show that modular forms of fractional weights on principal congruence subgroups of odd levels, which are found by T. Ibukiyama, naturally appear as characters being multiplied $\eta^{c_{\text{eff}}}$ of the so-called minimal models of…

In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…

Let \{M_{r,s}\}_{0< r < p, 0< s < p'} be the irreducible Virasoro modules in the $(p,p')$-minimal series. In our previous paper, we have constructed a monomial basis of \oplus_{r=1}^{p-1}M_{r,s} in the case of $1<p'/p<2$. By `monomials' we…

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…

Motivated by the necessity to include so-called logarithmic operators in conformal field theories (Gurarie, 1993) at values of the central charge belonging to the logarithmic series c_{1,p}=1-6(p-1)^2/p, reducible but indecomposable…