The Canonical Solutions of the Q-Systems¶ and the Kirillov–Reshetikhin Conjecture |
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Authors: | Atsuo Kuniba Tomoki Nakanishi Zengo Tsuboi |
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Institution: | Institute of Physics, University of Tokyo, Tokyo 153-8902, Japan. E-mail: atsuo@gokutan.c.u-tokyo.ac.jp, JP Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan.?E-mail: nakanisi@math.nagoya-u.ac.jp, JP Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan.?E-mail: tsuboi@gokutan.c.u-tokyo.ac.jp, JP
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Abstract: | 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.
Received: 2 August 2001 / Accepted: 27 December 2001 |
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