Reprint of: Minimal affinizations as projective objects☆☆☆
Reprint of: Minimal affinizations as projective objects☆☆☆
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DOI：
10.1016/j.geomphys.2011.06.011
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发表时间：
2011-09
影响因子：
1.5
通讯作者：
Vyjayanthi Chari;Jacob Greenstein
中科院分区：
文献类型：
--
作者：
Vyjayanthi Chari;Jacob Greenstein
我们证明了经典型无扭量子仿射代数的Kirillov-Reshetikhin模到q=1的特殊化在适当的范畴中是投射的。这就给出了Kirillov-Reshetikhin模的一个统一特征公式。我们猜想，这些结果保持专业化的最小仿射与相应的最高权重的一些限制。讨论了极小仿射的q-特征标与Nakai和Nakanishi猜想的关系。我们在一些特殊情况下证明了这个猜想。这也导致我们猜想一个交替和公式的雅可比特鲁迪行列式。
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.