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Strings, paths, and standard tableaux

Strings, paths, and standard tableaux
Strings, paths, and standard tableaux
For the vacuum sectors of regime-III ABF models, we observe that two sets of combinatorial objects: the strings which parametrize the row-to-row transfer matrix eigenvectors, and the paths which parametrize the corner transfer matrix eigenvectors, can both be expressed in terms of the same set of standard tableaux. Furthermore, the momenta of the strings, the energies of the paths, and the charges of the tableaux are such that there is a weight-preserving bijection between the two sets of eigenvectors, wherein the tableaux play an interpolating role. This bijection is so natural, that we conjecture that it exists in general.
0217-751X
501
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Foda, Omar
2a923282-f6a5-4d02-88a7-4df1fafa5650
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Foda, Omar
2a923282-f6a5-4d02-88a7-4df1fafa5650

Dasmahapatra, Srinandan and Foda, Omar (1998) Strings, paths, and standard tableaux. International Journal of Modern Physics A, 13, 501.

Record type: Article

Abstract

For the vacuum sectors of regime-III ABF models, we observe that two sets of combinatorial objects: the strings which parametrize the row-to-row transfer matrix eigenvectors, and the paths which parametrize the corner transfer matrix eigenvectors, can both be expressed in terms of the same set of standard tableaux. Furthermore, the momenta of the strings, the energies of the paths, and the charges of the tableaux are such that there is a weight-preserving bijection between the two sets of eigenvectors, wherein the tableaux play an interpolating role. This bijection is so natural, that we conjecture that it exists in general.

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Published date: 1998
Organisations: Southampton Wireless Group

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Local EPrints ID: 264097
URI: https://eprints.soton.ac.uk/id/eprint/264097
ISSN: 0217-751X
PURE UUID: ae0cbbe0-92e7-48cd-aa5b-6c3a40ff5b9e

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Date deposited: 29 May 2007
Last modified: 18 Jul 2017 07:39

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Author: Omar Foda

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