2012/08/22 by Kanehisa Takasaki, Takasaki, Kanehisa
Mathematics · Physics and Astronomy · #17B65 #35Q58 #82B20 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA #msc:17B65 #msc:35Q58 #msc:82B20 #nlin.SI
paper · pdf · doi:10.48550/arxiv.1208.4497
10 pages, no figure, poster presentation at conference "Integrability in Gauge and String Theory" (August 20-24, 2012)
arxiv created 2012/08/22 · arxiv updated 2012/08/23
Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, "shift symmetries" of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition function of the modified model is shown to be a tau function of the 2D Toda hierarchy. We conjecture that this tau function belongs to a class of solutions (the so called Toeplitz reduction) related to the Ablowitz-Ladik hierarchy.