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- Title
AN ALGEBRAIC APPROACH TO VERTEX MODELS AND TRANSFER MATRIX SPECTRA.
- Authors
DEGUCHI, T.; MARTIN, P. P.
- Abstract
We analyse the transfer matrix spectra of vertex models associated with the Lie superalgebras gl(P|M) and sl(P|M) using the representation theory of the Hecke algebra Hn(q). We develop a terminology for discussing the Bethe ansatz computation of the spectrum from this perspective. Using representations coming from these vertex models we develop some new methods for dealing with the analysis of Hecke algebras in any specialisation, including roots of unity. We also discuss the construction and spectrum of fusion models from the viewpoint of representation theory, begining a classification of the spectrum and identifying some sectors with trivial spectrum. In particular we show that the spectrum of the sl(P|M) λ-fusion model is trivial if λP+1>M.
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 1992, Vol 7, p165
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X9200377X