Related papers: q-Virasoro constraints in matrix models
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric…
Starting from a detailed analysis of the structure of pathspaces of the ${\cal A}$-fusion graphs and the corresponding irreducible Virasoro algebra quotients $V(c,h)$ for the ($2,q$ odd) models, we introduce the notion of an admissible…
We investigate compressibility of the dimension of positive semidefinite matrices while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
We use the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras to reconsider some generic aspects of CFTs with the BMS${}_3$ algebra defined as a chiral symmetry. For unitarity theories, it is known that the extended symmetry…
Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via $q_R$-conformal symmetries in the…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\beta$. These dynamics describe for $\beta=2$ the time evolution of the eigenvalues of $N\times N$ random…
In this paper we study ternary algebras of third-order hypermatrices. By hypermatrix we mean a complex-valued variable with three indices, which is also called a three-dimensional matrix or spatial matrix. We assume that a hypermatrix is…
The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the…
We prove that all the correlation functions in the $(1,q)$ models are calculable using only the Virasoro and the $W^{(3)}$ constraints. This result is based on the invariance of correlators with respect to an interchange of the order of the…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within…
We construct collective field theories associated with one-matrix plus $r$ vector models. Such field theories describe the continuum limit of spin Calogero Moser models. The invariant collective fields consist of a scalar density coupled to…
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
To a given algebraic curve we assign an infinite family of quantum curves (Schr\"odinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model…