Current browse context:
math-ph
Change to browse by:
References & Citations
Mathematical Physics
Title: Integrable models from singly generated planar algebras
(Submitted on 23 Feb 2023 (v1), last revised 14 Aug 2023 (this version, v2))
Abstract: Not all planar algebras can encode the algebraic structure of a Yang--Baxter integrable model described in terms of a so-called homogeneous transfer operator. In the family of subfactor planar algebras, we focus on the ones known as singly generated and find that the only such planar algebras underlying homogeneous Yang--Baxter integrable models are the so-called Yang--Baxter relation planar algebras. According to a result of Liu, there are three such planar algebras: the well-known Fuss--Catalan and Birman--Wenzl--Murakami planar algebras, in addition to one more which we refer to as the Liu planar algebra. The Fuss--Catalan and Birman--Wenzl--Murakami algebras are known to underlie Yang--Baxter integrable models, and we show that the Liu algebra likewise admits a Baxterisation. We also show that the homogeneous transfer operator describing a model underlied by a singly generated Yang--Baxter relation planar algebra is polynomialisable, meaning that it is polynomial in a spectral-parameter-independent element of the algebra.
Submission history
From: Xavier Poncini [view email][v1] Thu, 23 Feb 2023 00:27:58 GMT (72kb)
[v2] Mon, 14 Aug 2023 03:11:41 GMT (117kb,D)
Link back to: arXiv, form interface, contact.