Related papers: W-representation of Rainbow tensor model

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only…

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

For coprime $p,q\in\mathbb{Z}_{\geq 2}$, the triplet vertex operator algebra $W_{p,q}$ is a non-simple extension of the universal Virasoro vertex operator algebra of central charge $c_{p,q}=1-\frac{6(p-q)^2}{pq}$, and it is a basic example…

The goal of this paper is to study the representation theory of a classical infinite-dimensional Lie algebra - the Lie algebra of vector fields on an N-dimensional torus for N > 1. The case N=1 gives a famous Virasoro algebra (or its…

We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models,…

We study a vertex operator algebra containing a tensor product of Ising models. It is a direct sum of code vertex operator algebra and its irreducible modules. Therefore, we classify all irreducible modules of code vertex operator algebras…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle…

We study the Virasoro constraints for moduli spaces of representations of quiver with relations by Joyce's vertex algebras. Using the framed Virasoro constraints, we construct a representation of half of the Virasoro algebra on the…

Consistently constrained WZWN models on G/{S x U(1)^n} is given by constraining currents of the WZWN models with G. Poisson brackets are set up on the light-like plane. Using them we show the Virasoro algebra for the energy-momentum tensor…

We construct vertex operator representations for the full (N+1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl(N)…

In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…

In the paper there are investigated various approximate representations of the infinite dimensional $\Bbb Z$--graded Lie algebras: the Witt algebra of all Laurent polynomial vector fields on a circle and its one-dimensional nontrivial…

We show that every unitary positive energy representation W of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli by bounded operators on the Hilbert space completion of W. We use this to show…

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…

Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but ``non-propagating'', term (tr[X])^2 to the Lagrangian.…

We present the irregular matrix model which has contains $\mathcal{W}_3$ and Virasoro symmetry. The irregular matrix model is obtained using the colliding limit of the Toda field theories and produces the inner product between irregular…

We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield…

The maximal subgroup of unipotent upper-triangular matrices of the finite general linear groups are a fundamental family of $p$-groups. Their representation theory is well-known to be wild, but there is a standard supercharacter theory,…