The Kirillov-Reshetikhin conjecture and solutions of T-systems

Details The Kirillov-Reshetikhin conjecture and solutions of T-systems The Kirillov-Reshetikhin conjecture and solutions of T-systems

2005-01-13

arxiv.org/abs/math/0501202v3

Journal fur die reine und angewandte Mathematik 596 (2006), 63--87

Mathematics

Quantum Algebra

23 pages ; accepted for publication in Journal fur die reine und angewandte Mathematik

Scientific paper

We prove the Kirillov-Reshetikhin conjecture for all untwisted quantum affine algebras : we prove that the character of Kirillov-Reshetikhin modules solve the Q-system and we give an explicit formula for the character of their tensor products. In the proof we show that the Kirillov-Reshetikhin modules are special in the sense of monomials and that their q-characters solve the T-system (functional relations appearing in the study of solvable lattice models). Moreover we prove that the T-system can be written in the form of an exact sequence. For simply-laced cases, these results were proved by Nakajima with geometric arguments which are not available in general. The proof we use is different and purely algebraic, and so can be extended uniformly to non simply-laced cases.

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