Related papers: Fusion rules for the Temperley-Lieb algebra and it…
Deuteron-triton (DT) fusion is the primary fusion reaction used in controlled fusion research, mainly for its relatively high reaction cross sections compared to other fusion options. Even so, to attain appreciable reaction probabilities…
We explicitly describe the category of modules of the Temperley-Lieb algebra $\mathrm{TL}_n(\beta)$ under specialization $\beta=0$ for even $n$ in terms of a quiver algebra, analogous to a result of Berest-Etingof-Ginzburg. In particular,…
The recent article [arXiv:2307.12552] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev's Toric Code and in Levin-Wen string net models, and gave a bulk boundary correspondence to describe bulk…
We propose a radiative lepton seesaw model with the ${\mathbb Z}_3$ Tambara-Yamagami fusion rule and gauged $B-L$ symmetry. The heavier right-handed neutral fermions ($N_R$) simultaneously contribute to the masses of charged-leptons and…
We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the…
The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test…
The Demazure character formula is applied to the Verlinde formula for affine fusion rules. We follow Littelmann's derivation of a generalized Littlewood-Richardson rule from Demazure characters. A combinatorial rule for affine fusions does…
This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in…
We introduce two new algebras that we call \emph{tied--boxed Hecke algebra} and \emph{tied--boxed Temperley--Lieb algebra}. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second…
A tame filtration of an algebra is defined by the growth of its terms, which has to be majorated by an exponential function. A particular case is the degree filtration used in the definition of the growth of finitely generated algebras. The…
In this paper we prove the fusion rules of $L(c_{1,q},0)$ for all $q\geq1$. Roughly speaking, we consider $L(c_{1,q},0)$ as the limitation of $L(c_{n,nq-1},0)$, where $n\rightarrow\infty$, and the fusion rules of $L(c_{1,q},0)$ follow as…
According to Kirillov's theory, the construction of a unitary irreducible representation of a nilpotent Lie group requires a precise computation of some polarizing subalgebra subordinated to a linear functional in the linear dual of the…
We study the category $\mathcal{F}_n$ of finite-dimensional integrable representations of the periplectic Lie superalgebra $\mathfrak{p}(n)$. We define an action of the Temperley--Lieb algebra with infinitely many generators and defining…
The subject of our study is the Kazhdan-Lusztig (KL) equivalence in the context of a one-parameter family of logarithmic CFTs based on Virasoro symmetry with the (1,p) central charge. All finite-dimensional indecomposable modules of the…
The tubal tensor framework provides a clean and effective algebraic setting for tensor computations, supporting matrix-mimetic features like Singular Value Decomposition and Eckart-Young-like optimality results. Underlying the tubal tensor…
We represent Feigin's construction [22] of lattice W algebras and give some simple results: lattice Virasoro and $W_3$ algebras. For simplest case $g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We find simplest…
We show how the fusion rules for an affine Kac-Moody Lie algebra g of type A_{n-1}, n = 2 or 3, for all positive integral level k, can be obtained from elementary group theory. The orbits of the kth symmetric group, S_k, acting on k-tuples…
In topological phases of matter, fusion rules dictate how anyonic topological charges combine. However, the transformation of quasiparticle mobility under fusion remains largely unexplored. In this letter, we reveal that restricted mobility…
Conventional derivations of phase boundaries from the Clausius-Clapeyron (CC) relation often employ the constant latent heat approximation to maintain analytical functions of the sublimation and boiling curves. To address the complex…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…