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We prove the Kirillov–Reshetikhin (KR) conjecture in the general case: for all twisted quantum affine algebras, we prove that the characters of KR modules solve the twisted  Q -system [ 20 ] and we get explicit formulas for the character of their tensor products (the untwisted case was treated in [ 16 ,  33 ,  34 ]). The proof provides several new developments for the representation theory of twisted quantum affine algebras, in particular on the twisted Frenkel–Reshetikhin  q -characters that we define (expected in [ 11 ,  12 ]) and on the parameterization of simple finite dimensional representations without Drinfeld presentation. We also prove the twisted  T -system [ 30 ]. As an application, we get a proof of explicit (q)-characters formulas conjectured in various papers. We prove an isomorphism of Grothendieck rings between a twisted quantum affine algebra and the corresponding simply-laced quantum affine algebra.

Kirillov–Reshetikhin Conjecture: The General Case