Minimal affinizations as projective objects

Abstract

We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov-Reshetikhin modules. We conjecture that these results holds for specializations of minimal affinization with some restriction on the corresponding highest weight. We discuss the connection with the conjecture of Nakai and Nakanishi on q-characters of minimal affinizations. We establish this conjecture in some special cases. This also leads us to conjecture an alternating sum formula for Jacobi-Trudi determinants.

25 pages

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• On multigraded generalizations of Kirillov-Reshetikhin modules
• On the extended T-system of type $C_3$
• Graded limits of minimal affinizations and Beyond: the multiplicty free case for type E6
• Tilting Modules in Truncated Categories
• Moving between weights of weight modules
• On the minimal affinizations of type $F_4$
• A combinatorial identity for the Jacobian of $t$-shifted invariants