Minimal affinizations as projective objects

Details Minimal affinizations as projective objects Minimal affinizations as projective objects

2010-09-22

arxiv.org/abs/1009.4494v1

J. Geom. Phys. 61 (2011), no. 3, 594-609

Mathematics

Quantum Algebra

25 pages

Scientific paper

10.1016/j.geomphys.2010.11.008

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.

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