Fusion hierarchies, T-systems, and Y-systems of logarithmic minimal models

Abstract

A Temperley-Lieb (TL) loop model is a Yang-Baxter integrable lattice model with nonlocal degrees of freedom. On a strip of width N ∈ ℕ, the evolution operator is the double-row transfer tangle D(u), an element of the TL algebra TLN(β) with loop fugacity β = 2 cos λ, λ ∈ ℝ. Similarly, on a cylinder, the single-row transfer tangle T (u) is an element of the so-called enlarged periodic TL algebra. The logarithmic minimal models LM(p; p) comprise a subfamily of the TL loop models for which the crossing parameter λ = (p' - p)π=pis a rational multiple of π parameterized by coprime integers 1 ≤ p 2 takes the form of functional relations for D(u) and T (u) of polynomial degree p. These derive from ..