Intertwiners and \ade Lattice Models

Details Intertwiners and \ade Lattice Models Intertwiners and \ade Lattice Models

1993-04-05

arxiv.org/abs/hep-th/9304009v2

Int.J.Mod.Phys. B7 (1993) 3649-3705

Physics

High Energy Physics

High Energy Physics - Theory

48 pages, Two postscript files included#

Scientific paper

10.1142/S0217979293003449

Intertwiners between \ade lattice models are presented and the general theory developed. The intertwiners are discussed at three levels: at the level of the adjacency matrices, at the level of the cell calculus intertwining the face algebras and at the level of the row transfer matrices. A convenient graphical representation of the intertwining cells is introduced. The utility of the intertwining relations in studying the spectra of the \ade models is emphasized. In particular, it is shown that the existence of an intertwiner implies that many eigenvalues of the \ade row transfer matrices are exactly in common for a finite system and, consequently, that the corresponding central charges and scaling dimensions can be identified.

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