Minimal affinizations as projective objects

作者：Chari Vyjayanthi; Greenstein Jacob^*

来源：Journal of Geometry and Physics, 2011, 61(3): 594-609.

DOI：10.1016/j.geomphys.2010.11.008

• Kirillov-Reshetikhin module
• Current algebra
• Minimal affinization

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.

• 出版日期2011-3