The SOS model partition function and the elliptic weight functions

2008/02/01 by S. Pakuliak, V. Rubtsov, A. Silantyev +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Physics of Superconductivity and Magnetism #math.QA #msc:17B37 #msc:81R10 #msc:81R50

paper · pdf · doi:10.1088/1751-8113/41/29/295204

21 pages, 5 figures, requires iopart package

arxiv created 2008/02/01 · openalex publication_date 2008/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalized a recent observation (Khoroshkin and Pakuliak 2005 Theor. Math. Phys. 145 1373) that the partition function of the six-vertex model with domain wall boundary conditions can be obtained from a calculation of projections of the product of total currents in the quantum affine algebra U q ( sl 2 ) in its current realization. A generalization is done for the elliptic current algebra (Enriquez and Felder 1998 Commun. Math. Phys. 195 651, Enriquez and Rubtsov 1997 Ann. Sci. Ecole Norm. Sup. 30 821). The projections of the product of total currents in this case are calculated explicitly and are presented as integral transforms of a product of the total currents. It is proved that the integral kernel of this transform is proportional to the partition function of the SOS model with domain wall boundary conditions.

Cited by

• Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
• Antiperiodic dynamical 6-vertex model by separation of variables II: functional equations and form factors

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