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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2006

The Kirillov-Reshetikhin conjecture and solutions of T-systems

Résumé

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.

Dates et versions

hal-00109925 , version 1 (26-10-2006)

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Citer

David Hernandez. The Kirillov-Reshetikhin conjecture and solutions of T-systems. Journal für die reine und angewandte Mathematik, 2006, 596, pp.63--87. ⟨10.1515/CRELLE.2006.052⟩. ⟨hal-00109925⟩
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