Related papers: Factorized Combinations of Virasoro Characters
Product forms of characters of Virasoro minimal models are obtained which factorize into $(2,\odd)\times(3,\even)$ characters. These are related by generalized Rogers-Ramanujan identities to sum forms allowing for a quasiparticle…
Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are…
We demonstrate that certain Virasoro characters (and their linear combinations) in minimal and non-minimal conformal models which admit factorized forms are manifestly related to the ADE series. This permits to extract quasi-particle…
We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series ($N=1$). Example of the corresponding ``finitizated" identities relating corner transfer matrix polynomials with…
Two sets of identities between unitary minimal Virasoro characters at levels $m=3,4,5$ are presented and proven. The first identity suggests a connection between the Ising and tricritical Ising models since the $m=3$ Virasoro characters are…
We prove a factorization-concentration result for characters of symmetric groups. This is then applied to the asymptotic behaviour of the decomposition of the tensor representations. There are connections with the Pastur-Marcenko…
We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the…
We present a ``natural finitization'' of the fermionic q-series (certain generalizations of the Rogers-Ramanujan sums) which were recently conjectured to be equal to Virasoro characters of the unitary minimal conformal field theory (CFT)…
We revisit the line of non-unitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension.…
Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field…
An effective theory designed to compute Virasoro identity blocks at large central charge, expressed in terms of the propagation of a reparametrization/shadow mode between bilocal vertices, was recently put forward. In this paper I provide…
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
Some identities between unitary minimal Virasoro characters at levels 3, 4 and 5 are shown to arise as a consequence of relations between Artin L-functions of different quadratic fields. The definitions and concepts of number theory…
We present and prove Rogers-Schur-Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model $M(p,p').$ The proof uses the continued fraction decomposition of $p'/p$ introduced by Takahashi and Suzuki for the…
Virasoro conformal blocks are expected to exponentiate in the limit of large central charge $c$ and large operator dimensions $h_i$, with the ratios $h_i/c$ held fixed. We prove this by employing the oscillator formulation of the Virasoro…
We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of pattern formations. The interaction is based on a pairwise…
A definition is offered of the factorial characters of the general linear group, the symplectic group and the orthogonal group in an odd dimensional space. It is shown that these characters satisfy certain flagged Jacobi-Trudi identities.…
We study the occurrence of factorization in polarized and unpolarized observables in coincidence quasi-elastic electron scattering. Starting with the relativistic distorted wave impulse approximation, we reformulate the effective momentum…
We show that, for a certain class of partitions and an even number of variables of which half are reciprocals of the other half, Schur polynomials can be factorized into products of odd and even orthogonal characters. We also obtain related…
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…