On State Counting and Characters

Abstract

We outline the relationship between the thermodynamic densities and quasi-particle descriptions of spectra of RSOS models with an underlying Bethe equation. We use this to prove completeness of states in some cases and then give an algorithm for the construction of branching functions of their emergent conformal field theories. Starting from the Bethe equations of D n type, we discuss some aspects of the Z n lattice models. 4/94

Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods

“…Signs of an even stronger connection were found by Melzer [10], who conjectured that finitizations of the fermionic character expressions, originating from TBA for the finitized ABF model, equal finitizations of the bosonic character expressions originating from CTM for the finitized ABF model. It has especially been this last result and its many generalizations to other solvable models [18][19][20][21][22][23][24][25][26], that has motivated our attempt to unify TBA and CTM approaches to solvable models.…”

The role of paths in Robinson–Schensted algorithm (RS), and Kerov, Kirillov and Reshetikhin bijection (KKR)

“…For the reason of conciseness we refer readers to [8] (in this conference) for some ground information about string configuration, and like previously we will continue with the notation established there. As we told earlier there is a bijection between paths and standard Young tableaux, and between standard Young tableaux and rigged configurations [2,4], as well. This fact implies the bijection between paths and rigged configuration [4].…”

“…As we told earlier there is a bijection between paths and standard Young tableaux, and between standard Young tableaux and rigged configurations [2,4], as well. This fact implies the bijection between paths and rigged configuration [4]. Lets restrict ourselfs to the case n = 2.…”

“…We intend to present the paths considered by Dasmahapatra [4] in terms of a standard Young tableau (Young diagram whose cells are occupied by integers that strictly increase along the rows and along the columns). One path presents formation of one irrep { } D l of the unitary group U(n) in decomposition of one of the dual actions B [6].…”

“…The first column of the Table 3 contains magnetic configurations, the second -the corresponding Young tableaux under the RS bijection [7], and the fourth -the rigged string configurations resulting from KKR bijection, for the case N = 6 and n = 2. Some valuable information about eigenstates of the Heisenberg Hamiltonian are provided by string configuration and therefore by the paths because we are able to write down the rigging of the string configuration from the path [4]. These two objects inform us, at the very begining, about the character of the solutions of the Heisenberg Hamiltonian.…”