Search arXiv⌕ Search

arXiv · 1509.08616

Q-operators for higher spin eight vertex models with an even number of sites

Abstract

We construct the Q-operator for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra, following Baxter's 1973 paper. As an application, we prove the sum rule for the Bethe roots.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Takashi Takebe. 2015-11-03. Q-operators for higher spin eight vertex models with an even number of sites. https://doi.org/10.1007/s11005-015-0813-7

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Birational Equivalences for Kac--Moody Borel Enveloping Algebras

A Coxeter ordering of the simple roots of a finite-rank Kac--Moody algebra determines a finite family of commuting real-root vectors. We prove that $U^{\geq0}(\mathfrak g)$ is birationally equivalent to $Z\otimes\mathbb A_n$, where $Z$ is the residual Coxeter centralizer, by identifying the Coxeter localization $U^{\geq0}(\mathfrak g)[\mathbf X^{-1}]$ with $Z\otimes\mathbb A_n[\mathbf x^{-1}]$. For symmetrizable Cartan matrices the residual algebra is generated by finite Coxeter windows and is finitely presented. For the generic quantum Borel with torus dual to the root lattice, we prove the analogous birational equivalence.

math.QA↗

A diagrammatic presentation for every pivotal pointed fusion category

We provide a generators and relations presentation of pivotal pointed fusion categories, $Vec(G,ω,π)$. Unlike the well-known skeletal model, our presentation is strict and allows multiple isomorphic objects. Our main tool is skein theory, which allows us to apply topological tools to understand the relations of morphisms in the category.

math.QA↗

The Kazhdan-Lusztig category of $\mathfrak{osp}_{1|2n}$ at irrational levels

We prove the Kazhdan-Lusztig correspondence for the Lie superalgebra $\mathfrak{osp}_{1|2n}$ at irrational levels, that is, we show the category $\mathrm{KL}_k^{\rm ev}(\mathfrak{osp}_{1|2n})$ of finite-length even ordinary modules for the affine vertex operator superalgebra of $\mathfrak{osp}_{1|2n}$ at level $k \in \mathbb{C} \setminus \mathbb{Q}$ is braided tensor equivalent to the category of finite-dimensional even weight modules for the quantum group of $\mathfrak{osp}_{1|2n}$ at parameter $q = e^{πi/(2k+2n+1)}$. We also prove that ${\rm KL}_k^{\rm ev}(\mathfrak{osp}_{1|2n})$ is braided tensor equivalent to the category ${\rm KL}_\ell^{\rm ns}(\mathfrak{so}_{2n+1})$ of finite-length ordinary modules with non-spinorial top level for the affine vertex operator algebra of $\mathfrak{so}_{2n+1}$ at level $\ell$ such that $ \frac{1}{\ell+ 2n-1} = \frac{1}{2k+2n+1} + 1 \ \ ({\rm mod}\ 2\mathbb Z).$ Consequently, by gluing vertex operator (super)algebras via tensor categories, we construct a few new families of simple conformal vertex (super)algebras, including the mixed kernel VOAs that were the missing ingredient for proving certain Feigin-Frenkel type dualities in previous work of the first-named author with Linshaw, Nakatsuka, and Sato.

math.QA↗