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\(t\)-analogs of \(q\)-characters of Kirillov-Reshetikhin modules of quantum affine algebras. (English) Zbl 1078.17008

The author proves the conjecture of A.N.Kirillov and N.Yu.Reshetikhin [J. Sov. Math. 52, No. 3, 3156–3164 (1990); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 160, 211–221 (1987; Zbl 0900.16047)] concerning the characters of certain finite-dimensional representations of the quantum affine algebra \(\mathbb{U}_q(\hat{\mathfrak{g}})\), where \(\hat{\mathfrak{g}}\) is an untwisted simply laced affine Lie algebra. The main ingredient of the proof is the theory of \(t\)-analogs for \(q\)-characters introduced by the author in [H. Nakajima, “\(t\)-analogs of \(q\)-characters of quantum affine algebras of type \(A_n,D_n\).” Kang, Seok-Jin (ed.) et al., Combinatorial and geometric representation theory. An international conference, Seoul, Korea, October 22-26, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 325, 141–160 (2003; Zbl 1098.17013)].

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
82B23 Exactly solvable models; Bethe ansatz
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References:

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