The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture

Details The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture

2001-05-17

arxiv.org/abs/math/0105145v2

Commun.Math.Phys. 227 (2002) 155-190

Mathematics

Quantum Algebra

37 pages, amslatex. Remarks in 5.7 expanded. References updated

Scientific paper

10.1007/s002200200631

We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite Q-systems according to the number of functions and equations. The finite Q-systems appear as the thermal equilibrium conditions (the Sutherland-Wu equation) for certain statistical mechanical systems. Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras. We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp. infinite) Q-system. As an application, we reformulate the Kirillov-Reshetikhin conjecture on the multiplicities formula of the KR modules in terms of the canonical solutions of Q-systems.

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