Related papers: Combinatorial aspects of boundary loop models
We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebra, its partial analogue, walled Brauer algebra, its partial analogue, Temperley-Lieb algebra, its…
This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…
We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the natural module…
Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under…
The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…
We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex $\Xi$. In the "flip theory," cells of $\Xi_\mathrm{flip}$ correspond to polygonal…
The Temperley-Lieb (TL) family of algebras is well known for its role in building integrable lattice models. Even though a proof is still missing, it is agreed that these models should go to conformal field theories in the thermodynamic…
Obtaining rigorous statistical guarantees for generalization under distribution shift remains an open and active research area. We study a setting we call combinatorial distribution shift, where (a) under the test- and…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
We construct and analyze a class of one-dimensional boundary Hamiltonians arising from two-dimensional symmetry-protected topological phases with $\mathbb{Z}_N^{\times 3}$ symmetry on a triangular lattice. Using a cohomology-based…
We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we…
The periodic Temperley-Lieb category consists of connectivity diagrams drawn on a ring with $N$ and $N'$ nodes on the outer and inner boundary, respectively. We consider families of modules, namely sequences of modules $\mathsf{M}(N)$ over…
It was studied the growth of Temperley-Lieb type algebras with orthogonal and commutative relations associated with 2-colored edges graphs. Depending on the structure of the graphs they can be finite-dimensional or to have linear or…
We study the combinatorial and algebraic properties of Nonnegative Matrices. Our results are divided into three different categories. 1. We show a quantitative generalization of the 100 year-old Perron-Frobenius theorem, a fundamental…
We study the two-boundary Temperley--Lieb $O(n)$ loop model on Kazhdan--Lusztig bases of type A and B. We obtain explicit expressions of the ground state of the two-boundary Temperley--Lieb Hamiltonian by means of a coideal subalgebra of…
We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a…
Consider a binary mixture model of the form $F_\theta = (1-\theta)F_0 + \theta F_1$, where $F_0$ is standard Gaussian and $F_1$ is a completely specified heavy-tailed distribution with the same support. For a sample of $n$ independent and…
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying…