Reprint of: Minimal affinizations as projective objects

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• 作者：Vyjayanthi Chari^a ; ^{vyjayanthi.chari@ucr.edu"" rel=""nofollow} ; Jacob Greenstein ; ^a ; ^{jacob.greenstein@ucr.edu"" rel=""nofollow}
• 关键词：Kirillov&#x2013 ; Reshetikhin module ; Current algebra ; Minimal affinization
• 刊名：Journal of Geometry and Physics
• 出版年：2011
• 出版时间：September 2011
• 年：2011
• 卷：61
• 期：9
• 页码：1717-1732
• 全文大小：314 K

文摘

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 hold 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.